AT-OEMO-BEG 2012 Problem 4

A segment $AB$ is given. We erect the equilateral triangles $ABC$ and $ADB$ above and below $AB$ . We denote the midpoints of $AC$ and $BC$ by $E$ and $F$ respectively. Prove that the straight lines $DE$ and $DF$ divide the segment $AB$ into three parts of equal length .