Answer
The period is $\frac{1}{3}$
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 $3\pi$, so the period is $\frac{\pi}{3\pi}=\frac{1}{3}$