IGO 2020 I2

Let $ABC$ be an isosceles triangle ( $AB = AC$ ) with its circumcenter $O$ . Point $N$ is the midpoint of the segment $BC$ and point $M$ is the reflection of the point $N$ with respect to the side $AC$ . Suppose that $T$ is a point so that $ANBT$ is a rectangle. Prove that $\angle OMT = \frac{1}{2} \angle BAC$ .

Proposed by Ali Zamani