$$3\sin^2 x - 3\cos x -6\sin x + 2\sin 2x + 3=0$$
has a solution $x = 0$. That means it has a factor of $\cos x - 1$. I tried to write the given equation has the form
$$(\cos x - 1)P(x)=0.$$
I am looking for the factor $P(x)$. How can I get Mathematica to find it?