## Task 3.

In triangle $A B C$, the angle at vertex $B$ is $120^{\circ}$. Let $A_{1}, B_{1}, C_{1}$ be points on the sides $\overline{B C}$, $\overline{C A}$, $\overline{A B}$, respectively, such that $A A_{1}$, $B B_{1}$, $C C_{1}$ are the angle bisectors of triangle $A B C$. Determine the angle $\varangle A_{1} B_{1} C_{1}$.