Answer
$y=\frac{\pi}{3}$
Work Step by Step
RECALL:
$y=\text{arccsc}{(x)} \longrightarrow \sin{y}=\frac{1}{x}$, $y$ is in the interval $[-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}]$
Thus, $y=\text{arccsc}{(\frac{2\sqrt3}{3})}$ implies that $\sin{y}=\frac{1}{\frac{2\sqrt3}{3}}=\frac{\sqrt3}{2}$.
Note that $\sin{(\frac{\pi}{3})}=\frac{\sqrt3}{2}$.
Therefore,
$y=\text{arccsc}(\frac{2\sqrt3}{3})\longrightarrow y=\frac{\pi}{3}$
