Concyclic Eccentric angles of an ellipse.

Question

If $\;\alpha, \; \beta,\; \gamma,\; \delta\;$ are eccentric anlges of four conclyclic points on the standard ellipse $\; \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ . Then $\alpha + \beta + \gamma + \delta =\; ?$

Answer 1

Hint:

The points with eccentric angles $\alpha$, $\beta$, $\gamma$ & $\delta$ are $(a\cos\alpha, b\sin \alpha)$, $(a\cos\beta, b\sin \beta)$, $(a\cos\gamma, b\sin \gamma)$ & $(a\cos\delta, b\sin \delta)$

I hope you can solve further by applying the condition of con-cyclic points which are the points of intersection of ellipse & its auxiliary circle.