Quadrilaterals & Polygons · Superchallenge problem

In parallelogram $ABCD$, point $E$ lies on side $\overline{BC}$ with $BE : EC = 1 : 2$. Segment $\overline{AE}$ meets diagonal $\overline{BD}$ at $F$. What fraction of the area of the parallelogram is the area of triangle $BEF$?