Number of values of θ in 0,2π for which at least two roots of equation x3−1+cosθ+sinθx2+cosθsinθ+cosθ+sinθx−sinθcosθ=0 are equal is

Roots are 1, cosθ and sinθ .Now two roots are equal ⇒sinθ=1 or cosθ=1 or sinθ=cosθ ⇒θ=π2,θ=0,2π or θ=π4or 5π4⇒there are 5 values of θ in0,2π.