Solve $2\sin^3x + \sin3x +3\sin^2x \cos x + \cos^3x=0$ $2\sin^3x + \sin3x +3\sin^2x\cos x + \cos^3x=0$
My try:
$$2\sin^3x +3\sin x - 4\sin^3x +\cos x(3\sin^2x+\cos^2x)=0 $$
$$ \cos x(2\sin^2x+1) - 2\sin^3x+3\sin x=0.$$
And then i have no idea.

Since
$$
\sin 3x=3\cos^2x\sin x-\sin^3x
$$
you actually have
$$
\sin^3x+3\sin^2x\cos x+3\sin x\cos^2x+\cos^3 x=0,
$$
or, using the binomial theorem,
$$
(\sin x+\cos x)^3=0.
$$
I'm sure you can take it from here.
