A result related to the properties of Dedekind Sums

Question

We know that for $a=1$, we have $D(1,b;c)=s(b,c)=\sum_{n \pmod c} ((\frac{n}{c}))((\frac{bn}{c}))$. We also have this following result that, when $b$ and $c$ are coprime integers, we have $s(b,c)=\frac{1}{4c}\sum _{n=1}^{c-1} \cot(\frac{\pi n}{c})\cot(\frac{\pi nb}{c})$.