Odd squares from Basel

Given Euler's result $\sum _{n=1}^{\infty }\frac{1}{n^2}=\frac{{\pi }^2}{6}$, evaluate $\sum _{n=1}^{\infty }\frac{1}{(2n-1{)}^2}=1+\frac{1}{9}+\frac{1}{25}+\cdots$.

Classical — the Basel problem, solved by L. Euler (1734)