Ramanujan Cos/Cosh Identity

$$\left[{1+2\sum_{n=1}^\infty {\cos(n\theta )\over \cosh(n\pi)... ...)}}\right]^{-2} = {2\Gamma^4({\textstyle{3\over 4}})\over \pi}$$

for all $\theta$, where $\Gamma(z)$ is the Gamma Function.