1. **State the problem:** Find two angles between 0° and 360° whose cosecant is -2. 2. **Recall the definition:** Cosecant is the reciprocal of sine, so $$\csc(\theta) = \frac{1}{\sin(\theta)}$$ 3. **Given:** $$\csc(\theta) = -2$$ 4. **Find sine:** $$\sin(\theta) = \frac{1}{\csc(\theta)} = \frac{1}{-2} = -\frac{1}{2}$$ 5. **Determine angles where sine is -1/2:** Sine is negative in the third and fourth quadrants. 6. **Reference angle:** $$\sin^{-1}\left(\frac{1}{2}\right) = 30^\circ$$ 7. **Find angles:** - Third quadrant: $$180^\circ + 30^\circ = 210^\circ$$ - Fourth quadrant: $$360^\circ - 30^\circ = 330^\circ$$ 8. **Answer:** The two angles are $$210^\circ$$ and $$330^\circ$$. These angles satisfy $$\csc(\theta) = -2$$ between 0° and 360°.