2. Solve the equation $2[\cos 2 x]-[\sin x]=3[\sin 4 x]$, where $[a]$ is the integer part of $a$, i.e., the greatest integer not exceeding $a$.
$$
\left[\begin{array}{l}
x \in\left(2 \pi n ; \frac{\pi}{8}+2 \pi n\right), n \in \mathbb{Z} \\
x=\left(\frac{\pi}{8}+2 \pi n ; \frac{\pi}{4}+2 \pi n\right], n \in \mathbb{Z} \\
x=\frac{3 \pi}{4}+2 \pi n, n \in \mathbb{Z}
\end{array}\right.
$$