help me please.. and please provide steps so

I can follow.

sec(2ϴ)=3... solve for all solutions on [0,2π]

well, you have

sec 2θ = 3
cos 2θ = 1/3
2θ = 1.231 or 2π-1.231

so, divide those by 2, and then add π to get all 4 solutions.