If \( a_{r}=\cos \frac{2 r \pi}{9}+i \sin \frac{2 r \pi}{9}, r=1,2,3, \ldots \ldots, i=\sqrt{-1} \), then determinant \(…

If \( a_{r}=\cos \frac{2 r \pi}{9}+i \sin \frac{2 r \pi}{9}, r=1,2,3, \ldots \ldots, i=\sqrt{-1} \),

then determinant \( \left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right| \) is equal to :

[JEE Main 2021, 31 Aug (Shift 1)]