1. **Problem:** Evaluate the integral $$\int_0^{\frac{\pi}{3}} \sec^2 \theta \, d\theta$$. 2. **Formula and rules:** Recall that the derivative of $\tan \theta$ is $\sec^2 \theta$. Therefore, the integral of $\sec^2 \theta$ is $\tan \theta + C$. 3. **Intermediate work:** $$\int \sec^2 \theta \, d\theta = \tan \theta + C$$ 4. **Evaluate definite integral:** $$\int_0^{\frac{\pi}{3}} \sec^2 \theta \, d\theta = \left[ \tan \theta \right]_0^{\frac{\pi}{3}} = \tan \frac{\pi}{3} - \tan 0$$ 5. **Calculate values:** $$\tan \frac{\pi}{3} = \sqrt{3}, \quad \tan 0 = 0$$ 6. **Final answer:** $$\sqrt{3} - 0 = \sqrt{3}$$ Thus, the value of the integral is $\sqrt{3}$.