Answer
Both $\tan θ$ and $\cot θ$ are periodic with period $\pi$.
Work Step by Step
Since
\begin{aligned}
&\tan (\theta+\pi)=\frac{\sin (\theta+\pi)}{\cos (\theta+\pi)}=\frac{-\sin \theta}{-\cos \theta}=\tan \theta\\
&\cot (\theta+\pi)=\frac{\cos (\theta+\pi)}{\sin (\theta+\pi)}=\frac{-\cos \theta}{-\sin \theta}=\cot \theta
\end{aligned}
Then both $\tan θ$ and $\cot θ$ are periodic with period $\pi$.
