θ-π/4=θ+π/4-π/2 is the fourth quadrant angle.
cos(θ+π/4)^2 = 1-sin(θ+π/4)^2
cos(θ+π/4) = 4/5
sin(θ-π/4)= sin(θ+π/4-π/2)=-cos(θ+π/4)=-4/5
cos(θ-π/4)= cos(θ+π/4-π/2)= sin(θ+π/4)= 3/5
tan(θ-π/4)= sin(θ-π/4)/cos(θ-π/4)=-4/3