If the system of equations x+(√ 2 sin α) y+(√ 2 cos α) z=0; x+( cos α) y+( sin α) z=0; x+( sin α) y-( cos α) z=0 has a non-trivial solution, then α…

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 $\displaystyle \alpha \in\left(0, \frac{\pi}{2}\right)$ is equal to :