KöMaL 2021 B5163

Triangle $ABC$ is right-angled at $C$. The right angle is divided $2:1$ by a line such that the smaller part is closer to the shorter leg. This line intersects hypotenuse $AB$ at $T$, and the circumscribed circle at $D$. What are the measures of the acute angles of the triangle if the feet of the perpendiculars dropped from $D$ onto the lines of the legs are collinear with $T$?