Let
\(A(\theta )=\int { sin(\theta +\sin { \theta ){ e }^{ \cos { \theta } } } d\theta }\)

and \(B(\theta )=\int { cos(\theta +\sin { \theta ){ e }^{ \cos { \theta } } } d\theta }\)

Where \(A(0)=-1\) and \(B(0)=0\)

Then find the *value* of the *expression* \(\frac { \ln { \left\{ { \left( A\left( \theta \right) \right) }^{ 2 }+{ \left( B\left( \theta \right) \right) }^{ 2 } \right\} } }{ \cos { \theta } }\)

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