sin^2 θ(1+cotθ)+cos^2θ(1+tanθ)=2
sin^2 θ(1+cosθ/sinθ)+cos^2θ(1+sinθ/cosθ)=2
sin^2 θ+sinθcosθ+cos^2θ+sinθcosθ=2
2sinθsosθ+1=2
sin2θ=1
θ=π/4
tanθ=1