8.316. $\sin ^{4} x-\sin ^{2} x+4(\sin x+1)=0$.

8.316. $\sin ^{4} x-\sin ^{2} x+4(\sin x+1)=0$.
## Solution.

From the condition we have

$$
\begin{aligned}
& \sin ^{2} x\left(\sin ^{2} x-1\right)+4(\sin x+1)=0 \\
& \sin ^{2} x(\sin x-1)(\sin x+1)+4(\sin x+1)=0 \\
& (\sin x+1)\left(\sin ^{3} x-\sin ^{2} x+4\right)=0
\end{aligned}
$$

From this,

1) $\sin x=-1, x=-\frac{\pi}{2}+\pi k=\frac{\pi}{2}(4 k-1), k \in Z$;
2) $\sin ^{3} x-\sin ^{2} x+4 \neq 0$.

Answer: $x=\frac{\pi}{2}(4 k-1), k \in Z$.