If the system of equations $$ \begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & \mathrm{x}+(\cos \alpha) \mathrm{y}+(\sin \alpha) \mathrm{z}=0 \\ & \mathrm{x}+(\sin \alpha) \mathrm{y}-(\cos \alpha) \mathrm{z}=0 \end{aligned} $$ has a non-trivial solution, then $\alpha \in\left(0, \frac{\pi}{2}\right)$ is equal to :