#### Answer

$\frac{\pi}{6}$, $\frac{5\pi}{6}$

#### Work Step by Step

$2\sin x+3=4$
$2\sin x=1$
$\sin x=\frac{1}{2}$
Referring to the unit circle and remembering that sine is positive in Quadrants I and II, we conclude that the only solutions in $[0, 2\pi)$ are $\frac{\pi}{6}$ and $\frac{5\pi}{6}$.