\[\sum_{n=0}^{\infty} \dfrac{ \cos \bigg( \dfrac{3 \pi}{5} \left(2n+1 \right) \bigg) + \cos \bigg( \dfrac{\pi}{5} \left(2n+1 \right) \bigg)}{{\left(2n+1 \right)}^2}\]

The infinite sum above can be represented as \(\dfrac{{\pi}^a}{b}\), where \(a\) and \(b\) are non co-prime positive integers. Find the value of \(\dfrac ba\).

This problem is inspired from Ishan Singh.

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