Find the value of $ \begin{vmatrix} 1+2\omega^{100}+\omega^{200} & \omega^2 & 1 \\ 1 & 1+\omega^{100}+2\omega^{200} & \omega \\ \omega & \omega^2 & 2+\omega^{100}+\omega^{200} \end{vmatrix} $ where `omega` is the imaginary cube root of unity.