RMO 2019 Problem 2

Let $ABC$ be a triangle with circumcircle $\Omega$ and let $G$ be the centroid of triangle $ABC$ . Extend $AG, BG$ and $CG$ to meet the circle $\Omega$ again in $A_1, B_1$ and $C_1$ . Suppose $\angle BAC = \angle A_1 B_1 C_1, \angle ABC = \angle A_1 C_1 B_1$ and $\angle ACB = B_1 A_1 C_1$ . Prove that $ABC$ and $A_1 B_1 C_1$ are equilateral triangles.