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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