8.152. $\sin ^{2} 3 x=3 \cos ^{2} 3 x$.

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

8.152. $\sin ^{2} 3 x=3 \cos ^{2} 3 x$.
Solution.

Dividing this equation by $\cos ^{2} 3 x \neq 0$, we get

$\operatorname{tg}^{2} 3 x=3, \operatorname{tg} 3 x= \pm \sqrt{3}, 3 x= \pm \frac{\pi}{3}+\pi k, x= \pm \frac{\pi}{9}+\frac{\pi k}{3}=\frac{\pi}{9}(3 k \pm 1), k \in Z$

Answer: $\quad x=\frac{\pi}{9}(3 k \pm 1), k \in Z$