If ${\tan }^2\theta =1-e^2$, then the value of $\sec \theta +{\tan }^3\theta \text{cosec}\theta$ is

$\begin{array}{l}{\tan }^2\theta =1-e^2\\ \text{Add }“\text{1}”\text{ Both sides}\\ 1+{\tan }^2\theta =2-e^2\\ {\sec }^2\theta =(2-e^2)\Rightarrow \sec \theta ={(2-e^2)}^{\frac{1}{2}}\\ \sec \theta +{\tan }^3\theta \text{\hspace{0.17em}cosec}\theta =\sec \theta +{\tan }^2\theta \times \frac{\sin \theta }{\cos \theta }\times \text{ cosec}\theta \\ =\sec \theta +({\sec }^2\theta -1)\sec \theta \\ =\sec \theta (1+{\sec }^2\theta -1)\\ ={\sec }^3\theta \\ ={(2-e^2)}^{\frac{3}{2}}\end{array}$