sin6x+3sin4x.cos2x=0
find solution set
sin6x+3/2(sin6x+sin2x)=0
5sin6x+3sin2x=0
I got stuck here.
Plug that in for sin(3y). Then, let $\displaystyle u = \sin(y)$. You wind up with a cubic equation in $\displaystyle u$. Solve for $\displaystyle u$ (you have something for the form $\displaystyle au-bu^3=0$, so $\displaystyle u(a-bu^2)=0$ implies $\displaystyle u=0$ or $\displaystyle a-bu^2=0$). Once you solve for $\displaystyle u$, you have $\displaystyle u = \sin(y)$, so take arcsin of both sides. Then, you have $\displaystyle y = 2x$.