A geometry problem by Walid Mustafa

$In\quad \triangle ABC\quad in\quad the\quad adjoining\quad figure,\quad AD\quad and\quad AE\quad$ $trisect\quad \angle BAC.\quad The\quad lengths\quad of\quad BD,\quad DE\quad and\quad EC\quad are$ $2,\quad 3,\quad and\quad 6,\quad respectively.\quad$ $Find\quad the\quad length\quad of\quad the\quad shortest\quad side\quad of\quad \triangle ABC.$