Cool Geometry Problem

Let ABC be a triangle with an obtuse angle at $\angle$ ACB . The incircle of triangle ABC tangent to AB, Bc and CA at D, E and F , respectively. Let G be the midpoint of the side AB and let I be the incenter of triangle ABC. The line EF intersects the line AI and BI at M and N , respectively. Determine $\angle$ DNM = 78 degree Find $\angle$ DGM