DE-BUNDESWETTBEWERB 2023 Problem 7

Let $ABC$ be a triangle with incenter $I$ . Let $M_b$ and $M_a$ be the midpoints of $AC$ and $BC$ , respectively. Let $B'$ be the point of intersection of lines $M_bI$ and $BC$ , and let $A'$ be the point of intersection of lines $M_aI$ and $AC$ .

If triangles $ABC$ and $A'B'C$ have the same area, what are the possible values of $\angle ACB$ ?