an integral

Prompt

Evaluate and derive closed form for the integral and do not search online @Thinking $$ \int_0^\infty \frac{\sinh\left(2(\pi-\alpha)\nu\right) }{\sinh(\pi\nu)} \left( \frac{ \sinh(\beta\nu) \sinh(\theta\nu) }{ \sinh(\pi\nu) + \delta\sinh\left((\pi-2\alpha)\nu\right) } + \frac{ \cosh(\beta\nu) \cosh(\theta\nu) }{ \sinh(\pi\nu) - \delta\sinh\left((\pi-2\alpha)\nu\right) } \right) \sin(\nu t) \, \mathrm{d}\nu \, , $$ where $|\theta|,|\beta|\le \alpha \in (0,\pi]$ and $|\delta| \le 1$.