I have been stuck on a question for the past 40 minutes, it seems really simple. But, I can not get the right answer. Please help me, I don't like the feeling of an unsolved question!!!

I tried solutions like this:The angle x lies in the interval pi/2 <=x<=pi, and sin^2x = 8/9 . Without using a calculator, determine the value of cos x/2.

cos x/2 = cos 2(x/4) = 1-2sin^2(x/4) // What now? This is wrong right?