Difficult Geometry Problem

Let ABCD be a cyclic quadrilateral. Let P be the intersection of \(\overleftrightarrow{AD}\) and \(\overleftrightarrow{BC}\), and let Q be the intersection of \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\). Prove that the angle bisectors of angle DPC and angle AQD are perpendicular.

Thanks so much!