KöMaL 2021 C1697

Interior points $D$, $E$, $F$ are marked on sides $BC$, $CA$, $AB$ of a regular triangle $ABC$, respectively, such that $DEF$ is also a regular triangle. Then regular triangles $BDA'$ and $AEB'$ are drawn over the sides $BC$ and $AC$, respectively, on the outside. Prove that there exists a point on side $AB$ where each of the line segments $A'E$ and $B'D$ subtends a right angle.