If system of equations
\[
\begin{array}{l}
(\tan \alpha) x+(\cot \alpha) y+(8 \cos 2 \alpha) z=0...
If system of equations
\[
\begin{array}{l}
(\tan \alpha) x+(\cot \alpha) y+(8 \cos 2 \alpha) z=0 \\
(\cot \alpha) x+(8 \cos 2 \alpha) y+(\tan \alpha) z=0 \\
(8 \cos 2 \alpha) x+(\tan \alpha) y+(\cot \alpha) z=0
\end{array}
\]
have non-trivial solution, then \( \sin (4 \alpha) \) is equal to
(a) \( \frac{-\sqrt{3}}{2} \)
(b) -1
(c) \( \frac{-1}{2} \)
(d) \( \frac{1}{2} \)
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