Step 1:
First, we can split the integral into two parts as follows:
$$ \int^{\pi/4}_{0} \frac{1 + \cos^2 \theta}{\cos^2 \theta} \,d\theta = \int^{\pi/4}_{0} \frac{1}{\cos^2 \theta} \,d\theta + \int^{\pi/4}_{0} \frac{\cos^2 \theta}{\cos^2 \theta} \,d\theta $$
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