Trigonometric Equation solving

[Mark44]

Looks good.

A good thing to do is to check to confirm that sin(3x) = sin(x) for each of the seven values you have.

 

[epenguin]

Haven't followed this but you said trig identities. The trig identity to me most obviously relevant to problem #1 is the one for cos2x in terms of cos x, have you tried that?

(I think that gives you one of your (families of) solutions, and there is only one other real... if it's 20° as was said, that's' nothing very special or interesting to spend your time on IMHO).