8.170. $\cos 2 x+3 \sin x=2$.

8.170. $\cos 2 x+3 \sin x=2$. 

The translation is the same as the original text because it is a mathematical equation, which is universally understood and does not change when translated into another language.
## Solution.

We have $1-2 \sin ^{2} x+3 \sin x-2=0, 2 \sin ^{2} x-3 \sin x+1=0$. Solving this equation as a quadratic in terms of $\sin x$, we get $(\sin x)_{1}=\frac{1}{2}$,

$$
x_{1}=(-1)^{k} \frac{\pi}{6}+\pi k, k \in Z ;(\sin x)_{2}=1, x_{2}=\frac{\pi}{2}+2 \pi n=\frac{\pi}{2}(4 n+1) ; n \in Z
$$

Answer: $\quad x_{1}=(-1)^{k} \frac{\pi}{6}+\pi k ; x_{2}=\frac{\pi}{2}(4 n+1) \quad k, n \in Z$.