Geometry Problem 1607: Circle, Chords, Tangents, 60 Degree Angle

Circle Geometry Problem 1607: Find DE

Problem statement)

Let $\Omega$ be a circle and $A$, $B$, $C$ three points on it such that $AB=3$, $AC=5$, and $\angle BAC = 60^\circ$.

The tangents to $\Omega$ at $B$ and $C$ intersect at $D$. Let $E$ be the second point of intersection of the line $AD$ with $\Omega$.


Find the length of $DE$.