Verify That Each Equation Is an Identity $$\frac { 1 - \cot ^ { 2 } \theta } { 1 + \cot ^ { 2 } \theta } + 1 = 2 \sin ^ { 2 } \theta$$

Verify that each equation is an identity.
- $$\frac { 1 - \cot ^ { 2 } \theta } { 1 + \cot ^ { 2 } \theta } + 1 = 2 \sin ^ { 2 } \theta$$