(2cos²θ/2-1-sinθ)(√2sin(θ+π/4)=
=(cosθ-sinθ)(√2sin(θ+π/4))
=√2cos(θ+π/4)(√2sin(θ+π/4))
=2sin(2θ+π/2)=2cos2θ
tan2θ= - 2√2