Question 7
Consider a triangle $ABC$. Let $A_{1}$ be the symmetric point of $A$ with respect to the line $BC$, $B_{1}$ the symmetric point of $B$ with respect to the line $CA$, and $C_{1}$ the symmetric point of $C$ with respect to the line $AB$. Determine the possible set of angles of triangle $ABC$ for which $A_{1}B_{1}C_{1}$ is equilateral.
