DE-BUNDESWETTBEWERB 2019 Problem 7

Let $ABC$ be atriangle with $\overline{AC}> \overline{BC}$ and incircle $k$ . Let $M,W,L$ be the intersections of the median, angle bisector and altitude from point $C$ respectively. The tangent to $k$ passing through $M$ , that is different from $AB$ , touch $k$ in $T$ . Prove that the angles $\angle MTW$ and $\angle TLM$ are equal.