Easy integral

Calculus Level 5

If
π/6π/3dxsecx+cscx \displaystyle \int _{ \pi /6 }^{ \pi /3 }{ \frac { dx }{\sec x+\csc x } } can be represented in the form ab2+c2ln(d+efg) \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+ga+b+c+d+e+f+g

Detials and assumptions

1)a,b,c,d,e,f,ga,b,c,d,e,f,g are integers all less than 1010 . They need not to be distinct

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

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