(1)f(π/4)=sinπ/2-2(sinπ/4)^2=1-1=0
(2)f(x)=sin2x+cos2x-1=√2sin(2x+π/4)-1,所以最小正周期为2π/2=π
由-π/2+2kπ≤2x+π/4≤π/2+2kπ得：-3π/8+kπ≤x≤π/8+kπ,即f(x)的单调增区间为
[-3π/8+kπ,π/8+kπ]
(3)当sin(2x+π/4)=1时,f(x)取得最大值√2-1,此时2x+π/4=π/2+2kπ,所以x=π/8+kπ
x的集合为{x|x=π/8+kπ,k∈z}