AUSTRIAN-POLISH 1996 Problem 2

A convex hexagon $ABCDEF$ satisfies the following conditions:

1. $AB\parallel DE$ , $BC\parallel EF$ , and $CD\parallel FA$ .
2. The distances between these pairs of parallel lines are the same.
3. $\angle FAB = \angle CDE = 90^\circ$ Prove that the diagonals $BE$ and $CF$ of the hexagon intersect with angle $45$ degrees.

$\bullet$ Thank you dear Babis Stergiou for your translation. :P