Easy integral

Calculus Level 5

If
\[ \displaystyle \int _{ \pi /6 }^{ \pi /3 }{ \frac { dx }{\sec x+\csc x } } \] can be represented in the form \[ \frac { \sqrt { a } -b }{ 2 } +\frac { \sqrt { c } }{ 2 } \ln(\sqrt { d } +\sqrt { e } -\sqrt { f } -g)\] then find \(a+b+c+d+e+f+g\)

Detials and assumptions

1)\(a,b,c,d,e,f,g\) are integers all less than \(10\) . They need not to be distinct

2)\(a,c,d,e,f\) are not having any factor which is a perfect square.

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