In regular hexagon $ABCDEF$, points $W,X,Y,Z$ are chosen on sides $BC,CD,EF,FA$ respectively, so lines $AB,P_1,P_2,P_3,ED$ are parallel and equally spaced, where segment $ZW$ lies on line $P_1$ and segment $YX$ lies on line $P_3$. What is the ratio of the area of hexagon $WCXYFZ$ to the area of hexagon $ABCDEF$?