Please help me out with this indefinite integral.

Question

How to evaluate $$\int \frac{1+\sqrt{1+\tan(\theta)}}{1+\sqrt{1-\tan(\theta)}}d\theta$$ ?I am trying to evaluate this integral by multiplying the numerator and denominator by $(1-\sqrt{1-\tan(\theta)})$. Therefore we can write the above integral as $$\int \frac{(1+\sqrt{1+\tan(\theta)}(1-\sqrt{1-\tan(\theta)})}{(1+\sqrt{1-\tan(\theta)})(1-\sqrt{1-\tan(\theta)})}d\theta$$. Therefore we can write the above integral as $$\int \frac{(1+\sqrt{1+\tan(\theta)})(1-\sqrt{1-\tan(\theta)})}{\tan(\theta)}d\theta$$. After this step, we can write the above integral as $$\int\frac{(\sqrt{\cos(\theta)}+\sqrt{\cos(\theta)+\sin(\theta)})(\sqrt{\cos(\theta)}-\sqrt{\cos(\theta)-\sin(\theta)})}{\sin(\theta)}d\theta$$. Now after this step we can write the following integral as $$\int \frac{(\cos(\theta))+\sqrt{\cos(\theta)}(\sqrt{\cos(\theta)+\sin(\theta)}-\sqrt{\cos(\theta)-\sin(\theta)})-\sqrt{\cos(2\theta)}}{\sin(\theta)}d\theta$$. Now after this step, I can't evaluate the integral further. Please help me out with this integral.