If the points (−2,0),(−1,1/3)  and (cosθ,sinθ)  are collinear then the number of values of θ∈[0,2π]  is

If the points are collinear area of the triangle=012-201-1131cosθsinθ1 =0 -213-sinθ+1-sinθ-13cosθ=0⇒3sinθ−cosθ=2divide by 2 on both sides32sinθ-12cosθ=1 take cosπ6=32  and  sinπ6=12⇒sin(θ−π6)=1⇒θ−π6=π2θ=π2+π6=2π3