Interesting Geometry Problem

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.