If $\tan \theta-\cot \theta={cosec} \theta, 0^{\circ}<\theta<90^{\circ}$, then what is the value of $\frac{2 \tan \theta-\cos \theta}{\sqrt{3} \cot \theta+\sec \theta}$ ?

$\frac{3 \sqrt{3}-1}{6}$ $\frac{4 \sqrt{3}-1}{6}$ $\frac{2 \sqrt{3}-1}{3}$ $\frac{2(2 \sqrt{3}-1)}{3}$

$\frac{4 \sqrt{3}-1}{6}$