1. **State the problem:** We need to evaluate the function $f(x) = 1 + \tan(2x)$ at $x = \pi$. 2. **Recall the formula:** The function is given by $$f(x) = 1 + \tan(2x)$$ 3. **Substitute the value:** Replace $x$ with $\pi$: $$f(\pi) = 1 + \tan(2 \cdot \pi)$$ 4. **Simplify inside the tangent:** $$f(\pi) = 1 + \tan(2\pi)$$ 5. **Evaluate $\tan(2\pi)$:** Since tangent has period $\pi$, $$\tan(2\pi) = \tan(0) = 0$$ 6. **Calculate the final value:** $$f(\pi) = 1 + 0 = 1$$ **Final answer:** $f(\pi) = 1$