1. **State the problem:** Evaluate the integral $$\int (1 + \tan^2 \theta) \, d\theta$$. 2. **Recall the trigonometric identity:** The hint gives us the identity $$1 + \tan^2 \theta = \sec^2 \theta$$. 3. **Rewrite the integral using the identity:** $$\int (1 + \tan^2 \theta) \, d\theta = \int \sec^2 \theta \, d\theta$$ 4. **Recall the antiderivative formula:** The derivative of $$\tan \theta$$ is $$\sec^2 \theta$$, so $$\int \sec^2 \theta \, d\theta = \tan \theta + C$$ 5. **Write the final answer:** $$\boxed{\tan \theta + C}$$ This completes the solution for the first integral.