Find the derivative of $\displaystyle y = \left(-1 - \frac{csc \Theta}{2} - \frac{\Theta^2}{4}\right)^2$

So I'm guessing here you just use the chain rule to find the derivative. I get:

$\displaystyle y' = 2 \left(-1 - \frac{1}{2} csc \Theta - \frac{1}{4} \Theta^2\right)\left(\frac{1}{2}csc \Theta cot\Theta - \frac{1}{2}\Theta\right)$

If I know I did this much correct so far I can go on and simplify it.