2. Solve the equation $[\sin 2 x]-2[\cos x]=3[\sin 3 x]$, where $[a]$ is the integer part of $a$, i.e., the greatest integer not exceeding $a$.
$$
\begin{gathered}
x \in\left(2 \pi n ; \frac{\pi}{6}+2 \pi n\right) \cup\left(\frac{\pi}{6}+2 \pi n ; \frac{\pi}{4}+2 \pi n\right) \cup \\
\cup\left(\frac{\pi}{4}+2 \pi n ; \frac{\pi}{3}+2 \pi n\right), n \in \mathbb{Z}
\end{gathered}
$$