Deduce that $\sum_{n=1}^\infty\frac{1}{1+n^2}=\frac{1}{2}(\pi\coth\pi-1)\quad$

Question

I am having problems showing that $$\sum_{n=1}^\infty\frac{1}{1+n^2}=\frac{1}{2}(\pi\coth\pi-1)\quad $$ Here's my attept to this point: I tried to express each term using a partial fraction decomposition: $\frac1{1+ni}$ and $\frac1{1-ni}$. And I've been suggested from there that partial fractions can be expressed in terms of hyperbolic trigonometric functions. But i am stuck at this point. How to write a solution for this sum?