NIMCET 2026 — Mathematics PYQ

The number of values of $\theta$ in the interval $[0,2\pi ]$ for which the following homogeneous system of equations has a non-trivial solution is:

$$\{\begin{array}{l}x+(\sin \theta )y+(\cos \theta )z=0\\ x+(\cos \theta )y+(\sin \theta )z=0\\ x-(\sin \theta )y-(\cos \theta )z=0\end{array}$$