Interesting Geometry Problem

Geometry Level pending

Equilateral triangles $$ABE$$ and $$BCF$$ are erected externally on the sides $$AB$$ and $$BC$$ of a parallelogram $$ABCD$$. Let the angles in $$\triangle DEF$$ be $$\alpha,\beta,\theta$$ such that $$\alpha\leq\beta\leq\theta$$. Find $$\pi^{\theta(\alpha-\beta)}$$

Clarification: Treat all of these angles in degrees.

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