$\cos3x-\cos2x+\cos x=0$
$\Rightarrow2\cos2x\cos x-\cos 2x=0$
$\Rightarrow \cos 2x(2\cos x-1)=0$
$\Rightarrow \left[\begin{array}{l} \cos 2x=0 \\ \cos x=\dfrac{1}{2} \end{array} \right .$
$\Rightarrow \left[ \begin{array}{l} 2x=\dfrac{\pi}{2}+k\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{array} \right .$
$\Rightarrow \left[ \begin{array}{l} x=\dfrac{\pi}{4}+k\dfrac{\pi}{2}\\x=\pm\dfrac{\pi}{3}+k2\pi\end{array} \right .(k\in\mathbb Z)$
