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