Here's the problem: $$ e^{2 m i \cot ^{-1} p \cdot\left(\frac{p i+1}{p i-1}\right)^{m}}= $$
I got this from internet. I tried substituting $p=\cot(∆/2)$, managed to solve a bit of the problem but couldn't do it further.
Note: There isn't any remark about the domain of "$m$" and "$p$" in the question.