Point on an Ellipse for which sin(E) = sin(M)

Here is a question regarding motion on an ellipse.

Elliptical Motion follows Keplerâ€™s Equation:

E - e sin(E) = M

E and M are angles, measured in radians, and e is a constant: 0 < e < 1.
The period of motion is T.

In the first half of the motion, one point exists for which sin(E) = sin(M).
Find a simple expression for this point.

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