From previous parts of a rather long question, I have shown that $\displaystyle \sqrt{n}(2 arcsin \sqrt{\hat{p}} - 2arcsin \sqrt{p})$ converges in distribution to the standard normal distribution. The next part of the question is:

Use this fact to derive an approximate condence interval for $\displaystyle p$ known as the arcsine-interval, and compute this interval for some arbitrary confidence level, $\displaystyle n = 15, \hat{p}=0$.

It's just algebra, but I'm totally unsure about how to manipulate all these arcsines all over the place.