Find the general solution of the equation $\cos 3x + \cos x - \cos 2x = 0$.

Given equation: $\cos 3x + \cos x - \cos 2x = 0$
Using the identity $\cos A + \cos B = 2 \cos \left( \frac{A+B}{2} \right) \cos \left( \frac{A-B}{2} \right)$:
$2 \cos \left( \frac{3x+x}{2} \right) \cos \left( \frac{3x-x}{2} \right) - \cos 2x = 0$
$2 \cos 2x \cos x - \cos 2x = 0$
$\cos 2x (2 \cos x - 1) = 0$
This gives two cases:
Case $1$: $\cos 2x = 0$ $\Rightarrow 2x = (2n+1) \frac{\pi}{2}$ $\Rightarrow x = (2n+1) \frac{\pi}{4}$,where $n \in \mathbb{Z}$.
Case $2$: $2 \cos x - 1 = 0$ $\Rightarrow \cos x = \frac{1}{2} = \cos \frac{\pi}{3}$ $\Rightarrow x = 2n\pi \pm \frac{\pi}{3}$,where $n \in \mathbb{Z}$.