Easy integral

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.