Quadrilaterals & Polygons · Superchallenge problem

Rhombus $ABCD$ has side length $6$ and $\angle DAB = 60^\circ$. Point $E$ lies on side $\overline{AB}$ with $AE = 2$, and point $F$ lies on side $\overline{BC}$ with $BF = 2$. Find the area of triangle $DEF$. Give an exact answer.