Step 1:
First, we rewrite the integral in terms of secant and tangent functions:
$$\int \frac{\sec \theta \tan \theta}{\sec ^{2} \theta-\sec \theta} d \theta = \int \frac{1/\cos \theta \cdot \sin \theta/\cos \theta}{1/\cos^2 \theta - 1/\cos \theta} d \theta$$
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