KöMaL 2019 B5034

Prove that if none of the angles $\alpha$, $\beta$, $\gamma$, $\delta$ of a convex quadrilateral are right angles then $\tan \alpha+\tan \beta+\tan \gamma+\tan \delta=\tan \alpha\cdot\tan \beta\cdot\tan \gamma\cdot \tan \delta(\cot \alpha+\cot\beta+\cot\gamma+\cot\delta)$.