∵2/sin2θ -cosθ/sinθ
=1/sinθcosθ-cosθ/sinθ
=(1-cos^2θ)/sinθcosθ
= sin^2θ/sinθcosθ
=sinθ/cosθ
=tanθ
∵cosθ =-√2/3,θ ∈(π/2,π)
∴tanθ=-√14/2
∴2/sin2θ -cosθ/sinθ=-√14/2
∵2/sin2θ -cosθ/sinθ
=1/sinθcosθ-cosθ/sinθ
=(1-cos^2θ)/sinθcosθ
= sin^2θ/sinθcosθ
=sinθ/cosθ
=tanθ
∵cosθ =-√2/3,θ ∈(π/2,π)
∴tanθ=-√14/2
∴2/sin2θ -cosθ/sinθ=-√14/2