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