The opening doxological exclamation, said before the "O Heavenly King" and the set of "trisagion prayers," to my knowledge is "Glory to Thee (You), our God, glory to Thee (You)."
However I've repeatedly heard in Greek churches, "Glory to You, O Christ our God and our Hope, glory to you." I've also seen this in Korean Orthodox prayer books.
What's the deal with this?
Note: I'm aware that after the psalms are read in certain services, we say "Glory to Thee our God and our Hope, glory to Thee." I'm just not familiar with the practices of added "our hope" or "Christ our God" to the opening prayer of the trisagion prayers.