Transform the equation like this.... sin(90-3x)=sinx then the rest is easy.............
I don't understand why some people complicate things to such extend that their advises become useless for the students.
as I said cos3x=sin(90-3x) this is a formula of basic trigonometry no doubt about that.
then the equation is transformed to sin(90-3x) =sinx
this yields two formulas of general solutions..
1. 90-3x =(360)κ +x
2. 90-3x = (360)k+(180-x)
where k is an arbitrary integer...that is to be chosen to fit your given interval.....
no need to expand and get a qubic equation...........................