Geometry Level 3

$\large \left (1+\frac{b-c}{a} \right)^{a}+\left (1+\frac{c-a}{b}\right)^{b}+\left (1+\frac{a-b}{c}\right)^{c}=1$

Let $$a,b,c$$ be sides of a triangle. then find the number of triangles possible such that the equation above is fulfilled.

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