RO-NMO 2021 Problem 73

Let $ABC$ be a scalene triangle with $\angle BAC>90^\circ$. Let $D$ and $E$ be two points on the side $BC$ such that $\angle BAD=\angle ACB$ and $\angle CAE=\angle ABC$. The angle-bisector of $\angle ACB$ meets $AD$ at $N$, If $MN\parallel BC$, determine $\angle (BM, CN)$.

Petru Braica