Let's Go Outside

Geometry Level 4

There exist four circles which are each tangent to all three lines in the figure above. One of those circles is inside the triangle defined by these lines. (We are not interested in that one.) The centers of the remaining three form a triangle. Given \(a=52^\circ\) and \(b=75^\circ\), what is the angle of this triangle at the vertex directly opposite angle \(a\)?

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