y=2sin(π/4-x)=-2sin(x-π/4)
π/6≤x≤7π/6
π/6-π/4≤x-π/4≤7π/6-π/4
-π/12≤x-π/4≤11π/12
所以对于sin(x-π/4),当x-π/4=π/2时,sin(x-π/4)=1有最大值
当x-π/4=-π/12时,sin(x-π/4)=sin(-π/12)有最小值sin(-π/12)=-（√6-√2）/4
所以y的值域[-2,(√6-√2)/2]