Prove that: `cot^(-1)((ab+1)/(a-b))+cot^(-1)((bc+1)/(b-c))+cot^(-1)((ca+1)/(c-a))=0`.

Explanation

To prove the equation

\[ \cot^{-1}\left(\frac{ab+1}{a-b}\right) + \cot^{-1}\left(\frac{bc+1}{b-c}\right) + \cot^{-1\left(\frac{ca+1}{c-a}\right)} = 0, \]

we will use the property of inverse trigonometric functions and the identity for the sum of cotangent inverses.

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