Answer
$-6$
Work Step by Step
We know that $\cot$ has a period of $\pi$, hence $\cot(\theta)=\cot(\theta+k\pi)$ where $k$ is an integer.
Therefore,
$\cot(\theta)+\cot(\theta-\pi)+\cot(\theta-2\pi)\\
=\cot(\theta)+\cot(\theta)+\cot(\theta)\\
=-2+(-2)+(-2)\\
=-6$
