Didn't Constantine invent the trinity?
A lot of the topics covered in this thread would require more than a single post (or even a single thread) to explore fully, and that is especially true of this question. Still, for what it's worth I'll give an overview of what I understand the Orthodox position to be, at least as a start to answering the question.
As one might expect, the Orthodox would answer: "no, St. Constantine did not invent the concept of the trinity." I would argue that a case can be made for inklings of understanding of trinitarian theology in the Old Testament, an unveiling of such theology in the New Testament, and a firm affirmation of the trinity from the beginning among the Christian Church Fathers.
I will focus mostly on the New Testament and Church Fathers, but it is worth noting that it can be argued--and many Church Fathers did argue--that the trinity can be seen starting in the very first chapter of the Old Testament, where it says: "Let us make mankind in our image, in our likeness" (Gen. 1:26; some have claimed that Gen. 19:24 and Wis. 7:25-26, among other passages, can also be interpreted in a trinitarian manner).
In the New Testament the theology that had only been alluded to in the Old Testament became more clearly articulated. Thus the Gospel of John begins: "In the beginning was the Word, and the Word was with God, and the Word was God." (Jn. 1:1) And St. John continues to make clear who Jesus and the Holy Spirit are throughout the rest of his Gospel; as an example, St. John records the words of Jesus that: "All that belongs to the Father is mine." (Jn. 16:15)
The passages filling out the theology of the deity of Jesus and the Holy Spirit continue throughout the rest of the New Testament. For a few examples, Jesus Christ is said to be the power of God (1 Cor. 1:24), and is the image of God (Col. 1:15; Heb. 1:3; 2 Cor. 4:4), while the Spirit is the "holy Spirit of God" (Eph. 4:30), eternal, and essential in the salvific act of Christ (Heb. 9:14). When Ananias "lied to the Holy Spirit," this also means that he had "not lied just to human beings but to God" (Acts 5:3-4)
All of this trinitarian theology is very important because only God can save us. It is true that created beings can be used by God to help lead us to salvation, e.g. through preaching or teaching or correction (1 Tim. 4:15-16; James 5:19-20; etc.). Nonetheless, created beings could never impart grace to us, so when St. Paul says: "Grace be unto you, and peace, from God our Father, and from the Lord Jesus Christ," (1 Cor. 1:3; 2 Cor. 1:2; Gal. 1:3; etc.), he is not simply giving a greeting, but also making a specific theological claim. So to with sanctification, as when St. Peter says: "Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied." (1 Pet. 1:2)
Another time we find the trinitarian idea--in this specific case the deity of Jesus--in Phil. 2:5-11: "In your relationships with one another, have the same mindset as Christ Jesus: Who, being in very nature God, did not consider equality with God something to be used to his own advantage; rather, he made himself nothing by taking the very nature of a servant, being made in human likeness. And being found in appearance as a man, he humbled himself by becoming obedient to death—even death on a cross! Therefore God exalted him to the highest place and gave him the name that is above every name, that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue acknowledge that Jesus Christ is Lord, to the glory of God the Father."
When St. Thomas says "My Lord and my God!" (Jn. 20:28) in the Gospel, we believe he is speaking not simply ecstatically and out of more emotion than sense, but really expressing with his soul the realization that just took hold of him.
Regarding Church Fathers, we find already by the first decades of the second century Christians interpreting Gen. 1:26 as speaking of Jesus Christ being present (Epistle of Barnabas, 5). Around AD 107, St. Ignatius of Antioch was speaking of Jesus Christ as God (Epistle to the Romans, 1 and 18). St. Justin Martyr also, writing in the mid-second century, repeatedly says that Jesus is God (First Apology, 63; Dialogue with Trypho, 36; etc.), and that Christians worship the Son and Holy Spirit (First Apology, 6). A few decades later St. Ireneaus continued this affirmation of trinitarian theology, for example speaking of how the Son and Holy Spirit are co-eternal and co-existing with the Father (Against Heresies 2.30.9; 4.20.1), among other thoughts. St. Clement of Alexandria, writing at the end of the second century, also speaks of the diety of Jesus, affirming that he was "both God and Man" (Exhortation to the Heathen, 1)
And such quotations could be continued throughout the third century and into the fourth, but those should suffice to show that the idea that both Jesus and the Holy Spirit were God was firmly in place, and not just something hinted at vaguely until Constantine came along and insisted that everyone accept that belief. (As a side note, I am not necessarily saying that all these Fathers quoted above would have said things in the same way that later Christians would, I am speaking here just of the basic truths given by the Apostles and held by the Church, not the manner of explanation, etc.)
The part St. Constantine played at the First Ecumenical Council, in Nicea, was not to introduce a new concept regarding the deity of Christ. In fact, the deity of Christ was not in dispute. What was disputed was whether Jesus Christ was a divine yet created being, as Arius taught, or was co-eternal, co-powerful, etc. with the Father and not a created being. The part St. Constantine played was in suggesting a term (homoousios) that meant something along the lines of "of the same substance/essence/being," as opposed to the preferences of others who said that Jesus was, for example, "of like substance." The striking thing about St. Constantine's suggestion was not the idea itself, but rather that a word which had not previously been used for this purpose, and which had actually been used in a theologically incorrect manner by some, should be adopted.
The word was also not biblical--something that has been criticized by some (then and now). However, the biblical language and passages were disputed, and there was an impasse when using only such terms and verses. Something needed to be introduced that would cut through and make the Christian belief clear.