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Calculus Level 4

\[\large \int_{- {\pi}/{2}}^{{\pi}/{2}} e^{x} \cos^2x \, dx\] Given that the integral above can be expressed as \( \displaystyle \frac{a}{b}\sinh \left( \frac{c}{d} \pi \right)\), where \(a,b,c\) and \(d\) are positive integers with \(\gcd(a,b) = \gcd(c,d) = 1\), find the value of \(a+b+c+d\).

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