complex numbers question ?

Been trying to work out this further maths question on complex numbers- it seems ok up to a point but then the markscheme gets really confusing and I cannot work out what they've done. I'd really appreciate it if someone can help me decipher it.
I get to (e^ix (e^2inx -1))/ (e^2ix -1) and this is on the marksheme immediately equated to (e^nix) sin(nx) / sinx
Am I missing something obvious??

"Centre" the numeator and denominator, by pulling out a factor like
(e^(i2x) - 1) = e^(ix) (e^(ix) - e*(-ix))
then the map to sin should be straightforward for each.