1. **State the problem:** Find the smallest positive root of the equation $$\sin 3x = -1$$ where $x$ is in degrees. 2. **Recall the sine function properties:** The sine function equals $-1$ at angles where the argument is $$270^\circ + 360^\circ k$$ for any integer $k$. 3. **Set the argument equal to these values:** $$3x = 270^\circ + 360^\circ k$$ 4. **Solve for $x$:** $$x = \frac{270^\circ + 360^\circ k}{3} = 90^\circ + 120^\circ k$$ 5. **Find the smallest positive root:** For $k=0$, $$x = 90^\circ$$ which is positive. 6. **Conclusion:** The smallest positive root of $$\sin 3x = -1$$ is $$\boxed{90}$$ degrees.