Angle Trisectors Of A Right Triangle

Geometry Level 5

Triangle $ABC$ has angles $\angle A=3\alpha, \angle B=90^\circ$ and $\angle C=3\gamma$ . Let $P$ be a point in segment $BC$ such that $\angle PAB=\alpha$ , and $Q$ be a point in segment $BA$ such that $\angle QCB=\gamma$ . Let $R$ be a point within the triangle such that $\angle RAC=\alpha$ and $\angle RCA=\gamma$ . If $\angle QRC=142^\circ$ , what is the measure (in degrees) of $\alpha$ ?