Prove the identities

1. $$\frac{{\sin }^2\theta }{1-\cos \theta }=1+\cos \theta$$
2. $$(3+3\sin \theta )(3\cos \theta {)}^{-2}=\frac{1}{3-3\sin \theta }$$
3. $$\frac{\cos \theta }{1-\sin \theta }=\tan \theta +\frac{1}{\cos \theta }$$