Geometry Level 3

Triangle $$ABC$$ has $$\angle BAC = 20 ^\circ$$ and $$\angle ACB = 75 ^\circ$$. $$P$$ is a point in the interior of triangle $$ABC$$. Points $$D, E$$ and $$F$$ lie on $$BC, CA$$ and $$AB$$, respectively, such that $$A, E, P, F$$ are concyclic and $$C, D, P, E$$ are concyclic. What is the measure (in degrees) of $$\angle DPF$$?

Details and assumptions

Points are concyclic if they lie on a circle.

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