Answer
The period is $\frac{2\pi}{3}$
Work Step by Step
To find the period, one must first find $b$ in the base equation of cosecant functions $f(x)=a\cdot csc(b(x-c))+d$, then use $\frac{2\pi}{b}$. In this case, $b$ is $3$, so the period is $\frac{2\pi}{3}$