If normals at the points of and ellipse whose eccentric angles are $\alpha$, $\beta$, $\gamma$ and $\delta$ meet in a point, show that $\sin(\beta+\gamma) +\sin(\gamma+\alpha)+\sin(\alpha+\beta)$ = $0$
I started by writing normal equations in the parametric form at $\alpha$, $\beta$, and $\gamma$ and applied the condition of concurrency for the three lines but not getting the desired result.