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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