Let $m$ and $n$ be odd integers. Determine $$\sum_{k=1}^\infty \frac{1}{k^2}\tan\frac{k\pi}{m}\tan \frac{k\pi}{n}.$$

Compute tan^-1(1) -tan^-1(1/3) + tan^-1(1/5) – tan^-1(1/7) + … .