8. The acute angle that satisfies $2 \sin ^{2} x+\sin x-\sin 2 x=3 \cos x$ is = . $\qquad$
8. $\frac{\pi}{3}$.

Since $x$ is an acute angle, then $\cos x \neq 0$. Dividing both sides of the given equation by $\cos x$ yields $2 \sin x \cdot \tan x + \tan x - 2 \sin x = 3$, which simplifies to
$$
(2 \sin x + 1)(\tan x - 1) = 2 \text{.}
$$

Since the function $f(x) = (2 \sin x + 1)(\tan x - 1)$ is strictly increasing in $\left(0, \frac{\pi}{2}\right)$, and $f(x) = 2 = f\left(\frac{\pi}{3}\right)$, it follows that $x = \frac{\pi}{3}$.