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Geometry Level pending

In triangle ABC, AB = 1 and AC = 2. Suppose there exists a point P in the interior of triangle ABC such that ∠P BC = 70◦ , and that there are points E and D on segments AB and AC, such that ∠BP E = ∠EP A = 75◦ and ∠AP D = ∠DP C = 60◦ . Let BD meet CE at Q, and let AQ meet BC at F. If M is the midpoint of BC, compute the degree measure of ∠MP F.

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