If $2\tan \theta =\sec \theta$ , then $4{\cot }^2\theta -3{\tan }^2\theta =$

$2\tan \theta =\sec \theta$

$\frac{2\sin \theta }{\cos \theta }=\frac{1}{\cos \theta }$

$2\sin \theta =1$

$\sin \theta =\frac{1}{2}$

$\sin \theta =\sin 30°$

$\theta =30°$

$4{\cot }^2\theta -3{\tan }^2\theta =4{\cot }^{2}30°-3{\tan }^{2}30°$

$=4\left({\sqrt{3}}^2\right)-3{\left(\frac{{\displaystyle 1}}{{\displaystyle \sqrt{3}}}\right)}^2$

$=4\times 3-1=12-1=11$