Integrate sqr.rt(2(1-cosx)) dx from 0 to 2pi using trig identities?

So far the solution has been pretty elusive. Any detail or hints you could provide would be greatly appreciated.



Thanks!
The trig identity you need is



sin(x/2) = (1 - cos(x))/2



Then



2(1 - cos(x)) = 4 sin(x/2)

[2(1 - cos(x))] = [4 sin(x/2)] = 2 | sin(x/2) |



For the interval (0, 2), sin(x/2)