Mad with triangle (Part 1)

Geometry Level pending

Let \(a,b,c\) denote the sides of a triangle, with opposite angles \(A,B,C\) respectively, and let \(\Delta\) denote the area of the triangle.

The value of \( \dfrac{\tan(A/2)}{(a-b)(a-c)} + \dfrac{\tan(B/2)}{(b-a)(b-c)} + \dfrac{\tan(C/2)}{(c-a)(c-b)} \) is equal to:

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