1. **State the problem:** Find all values of $A$ such that $\tan A = -\sqrt{3}$ with $0 \leq A \leq 720^\circ$. 2. **Recall the tangent values:** The tangent of an angle is $-\sqrt{3}$ at angles where the reference angle has tangent $\sqrt{3}$ but the sign is negative. 3. **Reference angle:** $\tan 60^\circ = \sqrt{3}$, so the reference angle is $60^\circ$. 4. **Tangent sign rules:** Tangent is positive in Quadrants I and III, negative in Quadrants II and IV. 5. **Find angles in the first rotation (0 to 360°):** - Quadrant II: $180^\circ - 60^\circ = 120^\circ$ - Quadrant IV: $360^\circ - 60^\circ = 300^\circ$ 6. **Find angles in the second rotation (360° to 720°):** Add $360^\circ$ to each angle found in the first rotation: - $120^\circ + 360^\circ = 480^\circ$ - $300^\circ + 360^\circ = 660^\circ$ 7. **Final answer:** The values of $A$ are $$A = 120^\circ, 300^\circ, 480^\circ, 660^\circ.$$