The set of equations $\lambda x-y+z\cos \theta =0$ ,$3x+y+2z=0$  , $\left(\cos \theta \right)x+y+2z=0$  for  $0\le \theta <\pi$ has non Trivial solution

$$\begin{gathered} \text{ where }\mathrm{A}=\left[\begin{array}{ccc}\lambda & -1& \cos \theta \\ 3& 1& 2\\ \cos \theta & 1& 2\end{array}\right],\mathrm{X}=\left[\begin{array}{l}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right],\mathrm{O}=\left[\begin{array}{l}0\\ 0\\ 0\end{array}\right] \\ For non-trivial solution \\ \Rightarrow D=0 \\ \begin{array}{r}\Rightarrow \left|\begin{array}{ccc}\lambda & -1& \cos \theta \\ 3& 1& 2\\ \cos \theta & 1& 2\end{array}\right|=0\end{array} \end{gathered}$$

$\mathrm{D}=\cos \mathrm{\theta }-{\cos }^2\mathrm{\theta }+6>0,\text{ Since }\mathrm{D}>0$ only trivial solution is possible

$\text{ Hence, there is no value of }\theta \text{ and }\lambda \text{ for non-trivial solution}$