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Calculus Level pending

The integral \( \int _{0}^{ -\ln {2 }}{ \frac { dx }{ 8e^x + 2e^{-x} } } \) can be expressed as \(\frac { \alpha \arctan { (\frac { \beta }{ \gamma })- \pi } }{ \delta } \) where \(\alpha\), \( \beta\), \( \gamma\), \( \delta \) are all positive integers and \(\beta\) and \( \gamma\) are coprime.

Find the value of \(\alpha + \beta + \gamma + \delta \)

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