If $2 \sin \theta-8 \cos ^2 \theta+5=0,0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\tan 2 \theta+{cosec}~2 \theta)$ ?

$3 \sqrt{3}$ $\frac{4 \sqrt{3}}{3}$ $2 \sqrt{3}$ $\frac{5 \sqrt{3}}{3}$

$\frac{5 \sqrt{3}}{3}$