Answer
$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{2\pi}{3}+2n\pi$
Where n is an integer.
Work Step by Step
$\sqrt 3~csc~x-2=0$
$\sqrt 3~csc~x=2$
$csc~x=\frac{2}{\sqrt 3}$
$csc~x=\frac{2}{\sqrt 3}·\frac{\sqrt 3}{\sqrt 3}=\frac{2\sqrt 3}{3}$
The period of $csc~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are:
$x=\frac{\pi}{3}$ and $x=\frac{2\pi}{3}$
Now, add multiples of $2\pi$ to each of the solutions:
$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{2\pi}{3}+2n\pi$
