Solve $$\sin(2x)+\cos(x)-2\sin(x)-1=0,\quad x\in[-\pi,\pi].$$
I tried to make this into a quadratic equation so that I could solve for $x$ by converting $\sin(2x)$ into $2\sin(x)\cos(x)$ and then rearranging it somehow. Am I on the right track or not? Both ways, could I be offered a hint to the problem first rather than answers? Thanks very much!