$\begin{align}  & {{\tan }^{4}}\theta +2{{\tan }^{2}}\theta +1=\tan \theta -{{\tan }^{3}}\theta \Rightarrow {{(1+{{\tan }^{2}}\theta )}^{2}}=\tan \theta (1-{{\tan }^{2}}\theta ) \\  & \Rightarrow \frac{\tan \theta (1-{{\tan }^{2}}\theta )}{{{(1+{{\tan }^{2}}\theta )}^{2}}}=1\Rightarrow \frac{\tan \theta }{1+{{\tan }^{2}}\theta }\times \frac{1-{{\tan }^{2}}\theta }{1+{{\tan }^{2}}\theta }=1 \\  & \Rightarrow \frac{1}{2}\sin 2\theta .\cos 2\theta =1\Rightarrow \sin 2\theta .\cos 2\theta =2 \\  & \Rightarrow 2\sin 2\theta \cos 2\theta =4\Rightarrow \sin 4\theta =4\Rightarrow -1\le \sin 4\theta \le 1 \\ \end{align}$ در نتیجه معادله جواب ندارد.