How cute is that triangle?

Geometry Level 4

In acute triangle \(ABC\), we have \(\angle CAB = 70^\circ\). \(D\) is the foot of the perpendicular from \(B\) to \(AC\), and \( \angle DBC = 30^\circ\). \(P\) is a point on line segment \(BD\) such that \( \angle PAB = 40^\circ\). What is the measure (in degrees) of \( \angle PCA\)?

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