I wasn't sure how to approach this problem, but I gave it a shot and now I'm stuck. Can someone please review what I have done.

Thanks

$\displaystyle {csc{(2a)} - cot{(2a)} = tan{(a)}$

$\displaystyle ={csc{(a+a)} - cot{(a+a)} $

$\displaystyle ={csc{a} + csc{a} - cot{a} + cot{a} $

$\displaystyle ={\frac{1}{\sin{a}}+ \frac{1}{sin{a}}} -{\frac{cos{a}}{\sin{a}}+ \frac{cos{a}}{sin{a}}} $

$\displaystyle ={\frac{2}{\sin{a}} -{\frac{{2}cos{a}}{\sin{a}} $