The value of the determinant $Δ=\begin{vmatrix}\sin θ&\cos θ&\sin 2θ\\\sin(θ+\frac{2π}{3})&\cos(θ+\frac{2π}{3})&\sin(2θ+\frac{4π}{3})\\\sin(θ-\frac{2π}{3})&\cos(θ-\frac{2π}{3})&\sin(2θ-\frac{4π}{3})\end{vmatrix}$, is

none of these

Applying $R_2 → R_2 + R_3$, we have,

$Δ=\begin{vmatrix}\sin θ&\cos θ&\sin 2θ\\-\sin θ&-\cos θ&-\sin 2θ\\\sin(θ-\frac{2π}{3})&\cos(θ-\frac{2π}{3})&\sin(2θ-\frac{4π}{3})\end{vmatrix}=0$