Infinite sums can be manipulated!

Algebra Level 3

\[\large \sum_{n=1}^\infty \frac 1{(2n-1)^2} \]

Given that \(\zeta (2) = \dfrac {\pi^2}6 \), find the value of the infinite sum above.

Notation: \(\displaystyle \zeta (s) = \sum_{n=1}^\infty \frac 1{n^s} \) for \(s \in \mathbb C \ \forall \ \Re (s) > 1\) denotes the Riemann zeta function.

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