If $\Omega$ is a complex cube root of unity, then $\sin\bigg\{(\omega ^{10}+ \omega^{23}) \pi -\large \frac{\pi}{4}\bigg\}=$

Question

\[\begin {array} {1 1} (1)\;\frac{1}{\sqrt 2} & \quad (2)\;\frac{1}{2} \\ (3)\;t & \quad (4)\;\frac{\sqrt 3}{2} \end {array}\]