If \[{ e }^{ (\sin ^{ 2 }{ x } +\sin ^{ 4 }{ x } +\sin ^{ 6 }{ x } +..........\infty )\ln { 2 } }\] for \(0<x<\frac { \pi }{ 2 } \) , satisfies the equation \({ x }^{ 2 }-9x+8=0\) The value of \(\frac { 1 }{ 1 +\tan { x } } \) is of the form \(\frac { \sqrt { a } -b }{ c } \) . Find the value of \(\frac { a+b+c }{ 2 } \)

**DETAILS**

**a** is a square-free number and pairwise **g.c.d.** of **a**,**b** and **c** is **1**

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