Answer
$0$
Work Step by Step
We know that $tan$ has a period of $\pi$, hence first we try and find a value where the argument is between $0$ and $\pi$. Therefore $cot(\frac{7\pi}{2})=cot(\frac{(7-2)\pi}{2})=cot(\frac{5\pi}{2})=cot(\frac{(5-2)\pi}{2})=cot(\frac{3\pi}{2})=cot(\frac{(3-2)\pi}{2})=cot(\frac{\pi}{2})=0.$
