Minimum value

Geometry Level 4

In a \(\Delta ABC \), find the minimum value of \(\displaystyle \frac { \sum { { \left( \cot { \frac { A }{ 2 } } \right) }^{ 2 } } { \left( \cot { \frac { B }{ 2 } } \right) }^{ 2 } }{ { \prod { \left( \cot { \frac { C }{ 2 } } \right) } }^{ 2 } }\)

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