Why not just solve for F in terms of C and t. Note C will get in the denominator so will have and also an in there and I think a multiple also.
You've been given that start. Now it's your turn to show some working. It's assumed you're familar with the compound angle formula for expanding sin (x + y) .... (if not, then I don't see why you'd be given a question like this to solve in the first place).
Thanks for the tip on expanding with the sum/difference formulas.
Next question: I can see in the previous that solving for coefficients "a" and "b" would net me coefficient "C", but I'm not exactly sure where that comes from. I mean, I know that sin^2(3t) + cos^2(3t) = 1, but how does asin(3t) + bcos(3t) = Ccos(3t+F) ?? and wouldn't the fact that "F" is in the parenthesis mess it up?
BTW, you misspelled familar(sic).
After 4 years of engineering school (which I'll assume included the odd maths course along the way) you should be familir with how to solve these two equations simultaneously (which you should carefully check).
Edit: I only just saw your above post but don't have time to review it right now.