1. **State the problem:** Find the exact value of $\tan(\theta)$ when $\theta = -\frac{3\pi}{2}$.\n\n2. **Recall the definition and properties:** The tangent function is defined as $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. It is undefined when $\cos(\theta) = 0$.\n\n3. **Evaluate sine and cosine at $\theta = -\frac{3\pi}{2}$:**\nSince $-\frac{3\pi}{2}$ is coterminal with $\frac{\pi}{2}$ (because $-\frac{3\pi}{2} + 2\pi = \frac{\pi}{2}$), we have:\n$$\sin\left(-\frac{3\pi}{2}\right) = \sin\left(\frac{\pi}{2}\right) = 1$$\n$$\cos\left(-\frac{3\pi}{2}\right) = \cos\left(\frac{\pi}{2}\right) = 0$$\n\n4. **Calculate tangent:**\n$$\tan\left(-\frac{3\pi}{2}\right) = \frac{\sin\left(-\frac{3\pi}{2}\right)}{\cos\left(-\frac{3\pi}{2}\right)} = \frac{1}{0}$$\nDivision by zero is undefined.\n\n5. **Conclusion:** $\tan\left(-\frac{3\pi}{2}\right)$ is undefined, so the answer is DNE.