How to show infinite solutions of linear equation system?

Question

For example we have α, β belongs to $\Bbb R$, then how to show that the following system of linear equations will have infinite many solutions whenever β belongs to $[−\sqrt 2,\sqrt2]$? $$\left\{ \begin{align} -x + \sin \alpha\,y - \cos\alpha\,z=0,\\ \beta\, x + \sin \alpha\,y + \cos\alpha\,z = 0,\\ x + \cos\alpha\,y + \sin \alpha\,)z= 0. \end{align}\right.$$