trigonometry - Trig Identity Proof $frac{1 + sintheta}{costheta} + frac{costheta}{1 - sintheta} = 2tanleft(frac{theta}{2} + frac{pi}{4}right)$

I've been working on this for like half an hour now and don't seem to be getting anywhere. I've tried using the double angle identity to write the LHS with $\theta/2$ and have tried expanding the RHS as a sum. The main issue I'm having is working out how to get a $\pi$ on the LHS or removing it from the right to equate the two sides.

$$\frac{1 + \sin\theta}{\cos\theta} + \frac{\cos\theta}{1 - \sin\theta} = 2\tan\left(\frac{\theta}{2} + \frac{\pi}{4}\right)$$

Answer

hint:

$$\begin{align} & \cos\theta = \cos^2(\theta /2) - \sin^2(\theta/2)= (\cos (\theta/2) +\sin (\theta/2))(\cos (\theta/2) - \sin (\theta/2)), \\[10pt] & 1 \pm\sin \theta = (\cos (\theta/2) \pm \sin(\theta/2))^2. \end{align}$$