(1) Find the monotonic increasing interval of f(x);

(2) If α is the second quadrant angle, f (α/3) = 4cos (α+π/4) cos2alpha/5, find the value of cosα-sinα.

(1) When 2kπ-π/2≤3x+π/4≤2kπ+π/2, f(x) monotonically increases: [2kπ/3-π/4, 2kπ/3+π/12];

(2)sin(α+π/4)= 4 cos(α+π/4)cos 2α/5，sin(α+π/4)/cos(α+π/4)=4cos2α/5，(sinα+cosα)/(cosα-sinα)= 4 cos 2α/5，(sinα+cosα)？ /(cos？ α-sin？ α)=4cos2α/5， 1+sin2α=4cos？ 2α/5=4/5-4sin？ 2α/5, (sin2α+1) (4sin2α+1) = 0, sin2α=- 1 or sin2α =-14, α is the second quadrant angle, and cos α-sinα.