Answer
$x=\{\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}\}$
Work Step by Step
$csc(3x)=1$
$\frac{1}{sin(3x)}=1$
$sin(3x)=1$
$3x=sin^{-1}(1)$
We know $sin(x)$ is positive in quardent $I$ and quardent $II$
The period of the sine function is $2\pi$
$3x=\frac{\pi}{2}\;\;\;\;or\;\;\;\;\;\;3x=2\pi+ \frac{\pi}{2}\;\;\;\;or\;\;\;\;\;\;3x=4\pi + \frac{\pi}{2}\;\;\;\;\;\;\;\;\;\; $
$x=\frac{\pi}{6}\;\;\;\;or\;\;\;\;\;\;x=\frac{5\pi}{6}\;\;\;\;or\;\;\;\;\;\;x=\frac{3\pi}{2}\;\;\;\;\;\;\;\;\;\;\;\;\;$
$x=\{\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}\}$