Points E and F are located on square ABCD so that ΔBEF is equilateral. What is the ratio of the area of ΔDEF to that of ΔABE?[asy]
pair A=origin, B=(1,0), C=(1,1), D=(0,1), X=B+2*dir(165), E=intersectionpoint(B--X, A--D), Y=B+2*dir(105), F=intersectionpoint(B--Y, D--C);
draw(B--C--D--A--B--F--E--B);
pair point=(0.5,0.5);
label("A", A, dir(point--A));
label("B", B, dir(point--B));
label("C", C, dir(point--C));
label("D", D, dir(point--D));
label("E", E, dir(point--E));
label("F", F, dir(point--F));[/asy]<spanclass=′latex−bold′>(A)</span>34<spanclass=′latex−bold′>(B)</span>23<spanclass=′latex−bold′>(C)</span>3<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>1+3