The vertex $E$ of square $EFGH$ is at the center of square $ABC$D. The length of a side of $ABCD$ is 1 and the length of a side of $EFGH$ is 2. Side $EF$ intersects $CD$ at $I$ and $EH$ intersects $AD$ at $J$. If angle $EID = 60^\circ$, what is the area of quadrilateral $EIDJ$?