Problem #WSP-5291

Problem

$ABC$ is a triangle. The circumscribed circle is the circle that touches all three vertices of the triangle $ABC$. It is also the smallest circle lying entirely outside the triangle. The center of the circumscribed circle is $D$.

The inscribed circle is the circle which touches all three sides of the triangle $ABC$. It is also the largest circle lying entirely inside the triangle. The center of the inscribed circle is $E$.

The points $D$ and $E$ are symmetric with respect to the segment $AC$. Find the angles of the triangle $ABC$.