# Arccot and Arctans!

Geometry Level 4

$\displaystyle\large \cot^{-1}\left[\dfrac{ab+1}{a-b}\right]+\cot^{-1} \left[\dfrac{bc+1}{b-c}\right]+\cot^{-1}\left[\dfrac{ca+1}{c-a}\right]$

If $$a,~b,~c$$ are distinct non zero numbers having same sign, then the expression above returns two distinct values, $$m$$ and $$n$$, find the value of $$m+n$$.

Note: This problem uses the convention $$0 < \cot^{-1}(x) < \pi$$ for the range of the inverse cotangent function.

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