The number of all possible values of $$\theta$$ , where $$0 < \theta < \pi$$. for which the system of equations
$$(y + z) \cos 3 \theta = (xyz) \sin 3\theta$$
$$x \sin 3 \theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z}$$
$$(xyz) \sin 3\theta = (y + 2z) \cos 3 \theta + y \sin 3 \theta$$
have a solution $$(x_0, y_0, z_0)$$ with $$y_0z_0 \leq 0$$, is