Question 7 - A-Level Maths

Show that $\frac { \tan \theta + 1 } { 1 + \cos \theta } + \frac { \tan \theta - 1 } { 1 - \cos \theta } \equiv \frac { 2 ( \tan \theta - \cos \theta ) } { \sin ^ { 2 } \theta }$.
Hence, showing all necessary working, solve the equation $$\frac { \tan \theta + 1 } { 1 + \cos \theta } + \frac { \tan \theta - 1 } { 1 - \cos \theta } = 0$$ for $0 ^ { \circ } < \theta < 90 ^ { \circ }$.