Answer
$$2\sec ^2\left(θ\right)$$
Work Step by Step
Simplifying the expression using trigonometric identities, we find:
$$\frac{1}{1-\sin \left(θ\right)}+\frac{1}{1+\sin \left(θ\right)} \\ \frac{2}{\left(-\sin \left(θ\right)+1\right)\left(\sin \left(θ\right)+1\right)} \\ \frac{2}{\cos ^2\left(θ\right)} \\ 2\sec ^2\left(θ\right)$$