How can I prove that $\sum\limits_{i=1}^\infty \frac{1}{(2i-1)^{2}} = \frac{π^2}{8}$? I have the series $$\sum\limits_{i=1}^\infty \frac{1}{i^{2}} = \frac{π^{2}}{6}$$
How can I prove that: $$\sum\limits_{i=1}^\infty \frac{1}{(2i-1)^{2}} = \frac{π^2}{8}$$
I have been looking for it all over the web, I am certain it is out there, but I am not too familiar with the mathematical terms in English. Any links or help would be appreciated.

Hint:
$$\sum_{i=1}^{\infty} \frac1{i^2} = \sum_{i=1}^{\infty} \frac1{(2i - 1)^2} +  \sum_{i=1}^{\infty} \frac1{(2i)^2}$$
