Let $ABC$ be an equilateral triangle.
$D$ is on $BC$ and $\angle BAD = 20^\circ$.
Also let $I_1$, $I_2$ be the inner centers of triangles $ABD$, $ACD$ respectively.
$E$ is a point making the triangle $I_1I_2E$ be equilateral ($D$ and $E$ are on the opposite side of the line $I_1I_2$.
Then what is the $\angle ADE$?
This is my question and I tried to find $4$ cyclic points or something like that, but I have no idea.
Please help me.