Let $ABC$ be an acute and scalene triangle. Points $D$ and $E$ are in the interior of the triangle so that $<$ $DAB$ $=$ $<$ $DCB$, $<$ $DAC$ $=$ $<$ $DBC$, $<$ $EAB$ $=$ $<$ $EBC$ and $<$ $EAC$ $=$ $<$ $ECB$. Prove that the triangle $ADE$ is a right triangle.