If $w$ is an imaginary cube root of unity, then the value of $\sin \{(w^{10}+w^{23})\pi -\large\frac{\pi}{4} \}4 is

Question

$\begin{array}{1 1} \large\frac{-\sqrt 3}{2} \\ \large\frac{-1}{\sqrt 2} \\ \large\frac{1}{\sqrt 2}\\\large\frac{-\sqrt 5}{2}\end{array}$