INMO 2021 Problem 5

In a convex quadrilateral $ABCD$ , $\angle ABD=30^\circ$ , $\angle BCA=75^\circ$ , $\angle ACD=25^\circ$ and $CD=CB$ . Extend $CB$ to meet the circumcircle of triangle $DAC$ at $E$ . Prove that $CE=BD$ .

Proposed by BJ Venkatachala