8.287. $\cos 2 x+\cos \frac{3 x}{4}-2=0$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

8.287. $\cos 2 x+\cos \frac{3 x}{4}-2=0$.
Solution.

$\cos 2 x+\cos \frac{3 x}{4}=2 \Leftrightarrow\left\{\begin{array}{l}\cos 2 x=1, \\ \cos \frac{3 x}{4}=1\end{array} \Leftrightarrow\left\{\begin{array}{l}2 x=2 \pi k, \\ \frac{3 x}{4}=2 \pi l,\end{array} \Leftrightarrow\right.\right.$
$\Leftrightarrow\left\{\begin{array}{l}x=\pi k, k \in Z, \\ x=\frac{8 \pi l}{3}, l \in Z .\end{array} \Rightarrow \pi k=\frac{8 \pi l}{3}, 3 k=8 l, k=8 m, l=3 m, x=8 \pi m, m \in Z\right.$.

Answer: $x=8 \pi m, m \in Z$.