1. **Stating the problem:** Given an angle $\theta$, can we find the largest and smallest angle coterminal with it? We need to understand the nature of coterminal angles. 2. **Definition and formula:** Coterminal angles differ by full rotations of $360^\circ$. Mathematically, angles coterminal with $\theta$ are given by: $$\theta + 360^\circ k$$ where $k$ is any integer (positive, negative, or zero). 3. **Important rule:** Since $k$ can be any integer, there are infinitely many coterminal angles both greater than and less than $\theta$. 4. **Conclusion:** Because there is no upper or lower bound on $k$, there is no largest or smallest coterminal angle. The set of coterminal angles extends infinitely in both directions. **Final answer:** No, it is not possible because there are infinitely many coterminal angles greater than or less than $\theta$.