Identity Crisis

Geometry Level pending

Consider \(cos\left( -\beta \right) =\frac { 4 }{ 5 }\) , where \(-\beta\) is in the fourth quadrant. Find the value of \(\frac { sin\left( \frac { 3\beta }{ 4 } \right) +sin\left( \frac { \beta }{ 4 } \right) }{ cos\left( \frac { 3\beta }{ 4 } \right) +cos\left( \frac { \beta }{ 4 } \right) } \)

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