Answer
$\frac{\pi}{3}$, $\frac{5\pi}{3}$
Work Step by Step
$2\tan (\frac{x}{2})-\csc x=0$
$2*\frac{1-\cos x}{\sin x}-\frac{1}{\sin x}=0$
Multiply both sides by $\sin x$:
$2(1-\cos x)-1=0$
$2-2\cos x-1=0$
$1-2\cos x=0$
$2\cos x=1$
$\cos x=\frac{1}{2}$
The only solutions in $[0, 2\pi)$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.
