1. **State the problem:** We need to find the exact value of $\tan \theta$ where $\theta$ is an angle in standard position and its terminal side passes through the point $(-1, -1)$. 2. **Recall the formula:** For a point $(x,y)$ on the terminal side of an angle $\theta$, $\tan \theta = \frac{y}{x}$. 3. **Apply the formula:** Here, $x = -1$ and $y = -1$, so $$\tan \theta = \frac{-1}{-1}$$ 4. **Simplify the fraction:** $$\tan \theta = \frac{\cancel{-1}}{\cancel{-1}} = 1$$ 5. **Interpretation:** The tangent of the angle is $1$, which is already in simplest radical form. **Final answer:** $$\boxed{1}$$