Integrate then differentiate?

Calculus Level 4

Given that \(a\) is a variable independent of the variable \(x,\) we define \(I\) as follows:

\[ \large I = \int_0^{\pi /2} \ln \left( \dfrac{1+a \sin x}{1 - a \sin x} \right) \dfrac {dx}{\sin x}. \]

For \(|a| < 1\), find the value of \( \dfrac{dI}{da} \) in terms of \(a\).

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