KöMaL 2024 C1809

Let point $B$ be chosen inside line segment $AC$. We draw isosceles triangles $ABS_1$, $BCS_2$ and $CAS_3$ with no common interior points, bases $AB$, $BC$ and $CA$, respectively, and base angles of $30^{\circ}$. Prove that triangle $S_1S_2S_3$ is equilateral.