Solution
= Solution
The double-angle identity $\cos(2x)=2\cos^2x-1$ reduces the equation to $\cos x(1+2\cos x)=0$. On the specified interval the <cosine> takes each of the values $0$ and $-1/2$ once, giving
$$
\boxed{x=\frac\pi2,\quad x=\frac{2\pi}3.}
$$