If the system of equations \(x+\left(\sqrt{2}\sin \alpha \right)y+\left(\sqrt{2}\cos \alpha \right)z=0\\ x+\left(\cos \a…

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

[JEE Main 2024, 4 Apr (Shift 1)]