In triangle $ABC$, find the smallest possible value of $$|(\cot A + \cot B)(\cot B +\cot C)(\cot C + \cot A)|$$
Problem
Source: Indonesia INAMO Shortlist 2010 G7
Tags: geometry, geometric inequality, trigonometry, inequalities
Source: Indonesia INAMO Shortlist 2010 G7
Tags: geometry, geometric inequality, trigonometry, inequalities
In triangle $ABC$, find the smallest possible value of $$|(\cot A + \cot B)(\cot B +\cot C)(\cot C + \cot A)|$$