"Over-ambitious Triangle"

In an acute triangle ABC, $O$ is the circumcenter , $H$ is the orthocenter and $G$ is the centroid.

Let $OD$ be perpendicular to $BC$ , and $HE$ be perpendicular to $CA$ , with $D$ on $BC$ and $E$ on $CA$ . Let $F$ be the midpoint of $AB$ .

Suppose the areas of triangles $ODC$ , $HEA$ and $GFB$ are equal. Find the sum of all possible values of angle $C$ (in degrees).