Prove that this equation is true.
sin22a-sin2a=sin3a x sina
Then you want to solve the equation for a.
My calculator comes up with 18 solutions. I would not be surprised if there were actually 22 possibles (thus leaving 4 complex solutions.) Generally an equation with in it will reduce to an nth degree polynomial so you would be stuck solving a 22nd degree polynomial equation, which is impossible to do in general. You are going to be stuck doing numerical approximations.
However notice that there is at least one nice solution: a = 0.
-Dan