Line from nowhere

Geometry Level 4

Let \(ABC\) be a right triangle with \(\angle ABC=90^\circ\). Let \(P\) be a point on segment \(AC\) such that \(\frac{AP}{PC}=\frac{3}{2}\) and let \(Q\) be a point on segment \(AB\) such that \(AQ=3\cdot QB\). If \(\angle AQP=2 \angle PQC\), what is the measure (in degrees) of \(\angle PQC\) ?

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