Internal Discussion-2!

If $\alpha$ , $\beta$ , $\gamma$ and $\delta$ are the eccentric angles of four concyclic points on the ellipse $\displaystyle\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ . Then $\alpha + \beta + \gamma + \delta = ?$

If general solution of the answer in $n$ is of the form $(m\cdot n+k)\times\left(\text{any known constant}\right)$ , give your answer as $(m+k)\times\left(\text{the known constant}\right)$