Let S=[-π, (π)/2)-{-(π)/2,-(π)/4,-(3 π)/4, (π)/4}. Then the number of elements in the set A={θ ∈ S: tan θ(1+√ 5 tan (2 θ))=√ 5 - tan (2 θ)} is \ \ \…

Let $\displaystyle S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$. Then the number of elements in the set $\displaystyle A=\{\theta \in S: \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}$ is \_\_\_\_.