If $2\tan \mathrm{\theta }-\cot \mathrm{\theta }=-1\text{ then }\mathrm{\theta }=$________

$$\begin{gathered} 2\tan \mathrm{\theta }-\cot \mathrm{\theta }=-1 \\ \Rightarrow 2{\tan }^2\mathrm{\theta }+\mathrm{tan\theta }-1=0 \\ \Rightarrow 2{\tan }^2\mathrm{\theta }+2\mathrm{tan\theta }-\mathrm{tan\theta }-1=0 \\ \Rightarrow 2\mathrm{tan\theta }\left(\mathrm{tan\theta }+1\right)-\left(\mathrm{tan\theta }+1\right)=0 \\ \Rightarrow \left(2\mathrm{tan\theta }-1\right)\left(\mathrm{tan\theta }+1\right)=0 \\ \Rightarrow \mathrm{tan\theta }=\frac{1}{2}; \mathrm{tan\theta }=-1 \end{gathered}$$
or $\mathrm{\theta }=\mathrm{n\pi }+\left(\frac{-\mathrm{\pi }}{4}\right)\text{ or }\mathrm{\theta }=\mathrm{m\pi }+\mathrm{\alpha }$
where , $\mathrm{m},\mathrm{n}\in \mathrm{Z}\text{ and }\tan \mathrm{\alpha }=\frac{1}{2}$