If \( \int e^{\sin \theta}\left(\sin \theta+\sec ^{2} \theta\right)...

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If \( \int e^{\sin \theta}\left(\sin \theta+\sec ^{2} \theta\right) d \theta \) is equal to \( f(\theta)+C \)
\( \mathrm{P}^{10: 0} \) (where \( \mathrm{C} \) is the constant of integration) and \( f(0)= \)

W 0 , then the value of \( f\left(\frac{\pi}{4}\right) \) is
(1) \( e^{\sqrt{2}} \)
(2) \( e^{\frac{1}{\sqrt{2}}} \)
(3) \( e^{2} \)
(4) \( e^{\frac{1}{2}} \)
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