find thereal value of Θ for which 1+isinΘ/(1-2icosΘ) is real

1+sinθ1-2icosθ1+sinθ1-2icosθ×1+2icosθ1+2icosθ1+2icosθ+sinθ+2icosθsinθ1+4cos2θ1+sinθ1+4cos2θ+2cosθ+2cosθsinθ1+4cos2θiIt is  purely real when 2cosθ+2cosθsinθ1+4cos2θ is 02cosθ+2cosθsinθ1+4cos2θ=02cosθ+2cosθsinθ=02cosθ1+sinθ=0cosθ=0 and sin θ=-1  sin θ = sin 3π2θ = 2n+1π2   and θ =  + -1n3π2

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