tan(θ+π/4)
=[sin(θ+π/4)]/[cos(θ+π/4)]
=(√2/2sinθ+√2/2cosθ)/(√2/2cosθ-√2/2sinθ)
=(cosθ+sinθ)/(cosθ-sinθ)
=-2
∴cosθ+sinθ=-2(cosθ-sinθ)
cosθ+sinθ=-2cosθ+2sinθ
sinθ=3cosθ
∵sin²θ+cos²θ=1
∴10cos²θ=1
cos²θ=1/10