The set of equations $\mathrm{\lambda x}-\mathrm{y}+(\cos \mathrm{\theta })\mathrm{z}=0,3\mathrm{x}+\mathrm{y}+2\mathrm{z}=0$, $(\cos \mathrm{\theta })\mathrm{x}+\mathrm{y}+2\mathrm{z}=0,0\le \mathrm{\theta }<2\mathrm{\pi }$, has non-trivial solution(s)

for only one value of $\mathrm{\lambda }$ and all values of $\mathrm{\theta }$

for no value of $\mathrm{\lambda }$ and $\mathrm{\theta }$

for all values of $\mathrm{\lambda }$ and only two values of $\mathrm{\theta }$

for all values of $\mathrm{\lambda }$ and $\mathrm{\theta }$