calculus - Prove $sin a=int_{-infty}^{infty}cos(ax^2)frac{sinh(2ax)}{sinh(pi x)} operatorname dx$

Derive the integral representation

$$\sin a=\int_{-\infty}^{\infty}\cos(ax^2)\frac{\sinh(2ax)}{\sinh(\pi x)}dx$$
for $|a|\le \pi/2$.