sin(π/8)^4-cos(π/8)^4
=[sin(π/8)^2-cos(π/8)^2][sin(π/8)^2+cos(π/8)^2]
=sin(π/8)^2-cos(π/8)^2
=-[cos(π/8)^2-sin(π/8)^2]
=-cos(2*π/8)
=-cos(π/4)
=-√2/2