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 \(ABC\).