1. **Problem:** Find the exact value of $\sin\left(\frac{7\pi}{6}\right)$. 2. **Recall:** The reference angle for $\frac{7\pi}{6}$ is $\frac{7\pi}{6} - \pi = \frac{\pi}{6}$. 3. **Special Triangle:** The $30^\circ$-$60^\circ$-$90^\circ$ triangle has sides ratio $1 : \sqrt{3} : 2$. For $\sin(\theta)$, it equals opposite/hypotenuse. For $\frac{\pi}{6}$ (30°), $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$. 4. **Quadrant:** $\frac{7\pi}{6}$ is in the third quadrant where sine is negative. 5. **Answer:** Therefore, $$\sin\left(\frac{7\pi}{6}\right) = -\sin\left(\frac{\pi}{6}\right) = -\frac{1}{2}.$$ **Final answer:** $-\frac{1}{2}$