1. **Problem:** Find the general solution of the equation $\cot \theta = 0$. 2. **Formula and rules:** Recall that $\cot \theta = \frac{\cos \theta}{\sin \theta}$. The cotangent function is zero where the cosine is zero and sine is nonzero. 3. **Solution:** $$\cot \theta = 0 \implies \frac{\cos \theta}{\sin \theta} = 0 \implies \cos \theta = 0$$ 4. **Values of $\theta$ where $\cos \theta = 0$:** $$\theta = \frac{\pi}{2} + n\pi, \quad n \in \mathbb{Z}$$ 5. **Explanation:** The cosine function is zero at odd multiples of $\frac{\pi}{2}$, so the general solution is all angles of the form above. **Final answer:** $$\boxed{\theta = \frac{\pi}{2} + n\pi, \quad n \in \mathbb{Z}}$$