So for 1 - 9sin^2(2x), for x is an element of (0, pi):

Note that 0, pi is a full oscillation for sin(2x) (sub in 0 gives you 0, sub in pi gives you 2pi).

A full oscillation ranges from -1 to 1, but remember that the function is sin^2(2x). Since it's squared, the range of sin^2(2x) is described as 0 to 1.

Now, take 1 - 9(0) and 1 - 9(1) [subbing sin^2(2x) into the function], and that is your range: (-8, 1)