Lol...does Sydney Tech ever top anything...maybe Music last year, but that's hax - he probably played the piano longer than he's been breathing (with all due respect, it was a solid effort Desmond)
@ cyl, you can get to the final result by factoring out -i from the numerator
An alternative method below:
\frac{1-\cos\theta-i\sin\theta}{1+\cos\theta+i\sin\theta}\times \frac{1+\cos\theta-i\sin\theta}{1+\cos\theta-i\sin\theta} =...