Let \( \theta \in \left(0, \frac{\pi}{2}\right) \). If the system of linear equation.
\( (1 + \cos^2 \theta)x + \sin^2 \theta \, y + 4 \sin 3\theta \, z = 0 \)
\( \cos^2 \theta \, x + (1 + \sin^2 \theta) y + 4 \sin 3\theta \, z = 0 \)
\( \cos^2 \theta \, x + \sin^2 \theta \, y + (1 + 4 \sin 3\theta) z = 0 \)
Has a non-trivial solution, then the value of \( \theta \) is:
