Evaluate the following integrals:

i) 

ii) 

To evaluate these integrals, we can use the fact that \( \cos^2(\theta/2) \) and \( \sin^2(\theta/2) \) have simple expressions in terms of exponential functions. Specifically:

i) \( \cos^2(\theta/2) = \frac{1 + \cos(\theta)}{2} \)
ii) \( \sin^2(\theta/2) = \frac{1 - \cos(\theta)}{2} \)

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