Step 1:
First, we simplify the integral by using the trigonometric identities $\cot \theta = \frac{\cos \theta}{\sin \theta}$ and $\sec \theta = \frac{1}{\cos \theta}$:
$$\int_{\pi / 6}^{\pi / 3} \frac{\sin \theta \cot \theta}{\sec \theta} d \theta = \int_{\pi /
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