First of all .
You will need to use the identities and .
(with apologies to mr fantastic.)
There is no more general solution to sin(3x) + sin(2x) = 0 than this one.
The only place in trigonometry I have ever run into is when we are talking about the sine or cosine of an angle, not what the angle itself is. For example
where n is an integer, so I don't see how such an expression could get into the form for an angle.