^{4}(Ѳ) - 6cos

^{2}(Ѳ)sin

^{2}(Ѳ) + sin

^{4}(Ѳ) and that sin(4Ѳ) = 4cos

^{3}(Ѳ)sin(Ѳ) - 4cos(Ѳ)sin

^{3}(Ѳ).

I know that I first have to use De Moivre's theorem to find z

^{4}when z = cis(Ѳ), which gives me z

^{4}= cis(4Ѳ) = cos(4Ѳ) + sin(4Ѳ)i.

I also know that I need to expand [cos(Ѳ) + isin(Ѳ)]

^{4}, but that's where I get stuck. What's the best way to go about expanding this expression?

Thanks in advance.