I would like to derive the following expression for inverse cotangent:
$\cot^{-1} (z) = \frac{i}{2}[\ln(\frac{z-i}{z}) - \ln(\frac{z+i}{z})]$
But I don't want to take it as "definition" as this page (http://mathworld.wolfram.com/InverseCotangent.html) seems to suggest that, that is the 'standard' defintion (or at least a practical one).
In essence, I'm looking for a definition which only relies on tangent, inverse tangent, and cotangent.