= 1+sin2x-( 1-cos2x)

=sin2x+cos2x .

=√2sin(2x+π/4)

therefore

The minimum positive period is π.

Because x belongs to [three quarters, two thirds]

therefore

2x+π/4 belongs to [three quarters, four fifths].

therefore

When x= bisector, there is a maximum value of 1.

When x= quarter pie chart, there is a minimum value-1.

So the range is: [- 1, 1]