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The number of values of $θ$ in $[0, 3 π]$ satisfying $\sin^{3} θ - \cos^{3} θ + 1 + 3 \sin θ \cos θ = 0$

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Correct option is B

We have sin3θ+−cosθ3+1=3sinθ−cosθ.1⇒sinθ−cosθ+1=0 (∵a3+b3+c3=3abc ⇒a+b+c=0 or a=b=c)⇒cosθ−sinθ=1⇒12cosθ−12sinθ=12,⇒cosθ+π4=cosπ4⇒θ+π4=2nπ±π4⇒θ=2nπ or 2nπ−π2⇒θ=0,2π,3π2

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The number of values of θ in 0,3π satisfying sin3θ−cos3θ+1+3sinθcosθ=0

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The number of values of $θ$ in $[0, 3 π]$ satisfying $\sin^{3} θ - \cos^{3} θ + 1 + 3 \sin θ \cos θ = 0$