Let \(f\left( \theta \right) =\frac { \cot { \theta } }{ 1+\cot { \theta } }\) and \(\alpha +\beta =\frac { 5\pi }{ 4 }\). Then the value of \(f\left( \alpha \right) .f\left( \beta \right)\) can be written as \(\frac { a }{ b }\) where \(a\) and \(b\) are coprime integers. Find \(a+b\)

This question is a part of the set: Basic Trigo

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