Olympiad Geometry · Superchallenge problem

Triangle $T_0$ has angles $40^\circ$, $60^\circ$, and $80^\circ$. The bisectors of its three exterior angles (one at each vertex) form a triangle $T_1$. The same construction applied to $T_1$ gives $T_2$, and applied to $T_2$ gives $T_3$. Find the smallest angle of $T_3$.