Angle in an Extremal Triangle Configuration

Let $ABC$ be an equilateral triangle. Let $\overrightarrow{AB}$ be extended to a point $D$ such that $B$ is the midpoint of $AD$. A variable point $E$ is taken on the same plane such that $DE = AB$. If the distance between $C$ and $E$ is as large as possible, what is $\angle BED$ (in degrees)?