Question 24
Let $ABC$ be a triangle. A circle is tangent to segments $BC$, $CA$, $AB$ at points $D$, $E$, $F$, respectively. Given that the measures of $\angle CAB$, $\angle ABC$, $\angle BCA$ form an arithmetic progression in some order, prove that the measures of $\angle FDE$, $\angle DEF$, $\angle EFD$ also form an arithmetic progression in some order.