$\displaystyle cosec\theta= cot\frac{\theta}{2}-cot \theta$

$\displaystyle cosec 2 \theta=cot \theta-cot 2 \theta $

$\displaystyle

cosec 3 \theta = cot\frac{3 \theta}{2}- \cot 3 \theta

$

I am not sure if the above is possible . Can i do that for the \theta above ? By just altering the theta like that ?