If
\[
\theta \in \left( 0, \frac{\pi}{3} \right) \quad \text{and} \quad
\begin{vmatrix}
0 & -\sin^2 \theta & -2 - 4 \cos 6\theta \\
0 & \cos^2 \theta & -2 - 4 \cos 6\theta \\
1 & \sin \theta & \cos 2\theta
\end{vmatrix} = 0,
\]
then \( \theta \) is equal to: