I just realized that I made a mistake.
I used sin t and cos t and you wanted to use sin (3t) and cos (3t).
Just assume that was the case and do what I did below.
The problem:
y'' + 9y = 9sec^2(3t) 0 < t < pi/6
So I make it homogenous by setting y''+ 9y = 0
getting 3i repeating.... y = C1cos(3t)+C2sin(3t)
From there.. I'm not sure what to do with the 9sec^2(3t). Please help, I have a quiz later today, thanks!