If $\cot \theta +\tan \theta =m$ and $sec\theta -\cos \theta =n$ then which of the following is correct

$\cot \theta +\tan \theta =m\Rightarrow {\sec }^2\theta .=m\tan \theta -\left(1\right)$

$\sec \theta -\cos \theta =n\Rightarrow {\tan }^2\theta .=n\sec \theta -\left(2\right){\tan }^2\theta =n{\left(n{m}^2\right)}^{1/3}$

from (1) & (2) $\Rightarrow$ similarly ${\sec }^2\theta =m{\left(n^{2}m\right)}^{1/3}$ eliminate $\theta$