13. Find all solutions to the equation $\cos ^{2} x+\cos ^{2} 2 x+\cos ^{2} 3 x=1$.
13. The original equation can be transformed into $2 \cos ^{2} x+2 \cos ^{2} 2 x+2 \cos ^{2} 3 x=2, \cos 2 x+\cos 4 x+\cos 6 x=-1$, $\frac{\sin 7 x-\sin x}{2 \sin x}=-1, \sin 7 x=-\sin x, \sin 7 x+\sin x=0, \sin 4 x \cos 3 x=0, \sin 4 x=0$ or $\cos 3 x=0,4 x=k \pi$ or $3 x=k \pi+\frac{\pi}{2}, x=\frac{k \pi}{4}$ or $x=\frac{k \pi}{3}+\frac{\pi}{6}$. But when $k=4 m$, $x=m \pi$ is not a solution to the original equation, so the solutions to the original equation are $x=m \pi \pm \frac{\pi}{4}$ or $x=m \pi+\frac{\pi}{2}$ or $x=\frac{k \pi}{3}+\frac{\pi}{6}$.