$\begin{align}  & \frac{\sin \theta -2\cos \theta }{3\sin \theta -\cos \theta }=3\xrightarrow{\div \cos \theta }\frac{\frac{\sin \theta }{\cos \theta }-2\frac{\cos \theta }{\cos \theta }}{3\frac{\sin \theta }{\cos \theta }-\frac{\cos \theta }{\cos \theta }}=3\Rightarrow \frac{\tan \theta -2}{3\tan \theta -1}=3\Rightarrow \tan \theta -2=3(3\tan \theta -1) \\  & \Rightarrow \tan \theta -2=9\tan \theta -3\Rightarrow 9\tan \theta -\tan \theta =3-2\Rightarrow 8\tan \theta =1\Rightarrow \tan \theta =\frac{1}{8} \\ \end{align}$