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