15th Junior Turkish Mathematical Olympiad

A circle that passes through the vertex $A$ of a rectangle $ABCD$ intersects the side $AB$ at a second point $E$ different from $B$. A line passing through $B$ is tangent to this circle at a point $T$, and the circle with center $B$ and passing through $T$ intersects the side $BC$ at the point $F$. Show that if $\angle CDF=\angle BFE$, then $\angle EDF=\angle CDF$.