Let ${\tan }^{-1}\left(\mathrm{x}\right)\in \left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$, for $\mathrm{x}\in \mathrm{ℝ}$. Then the number of real solutions of the equation $\sqrt{1+\cos \left(2\mathrm{x}\right)}=\sqrt{2}{\tan }^{-1}(\tan \mathrm{x})$ in the set $\left(-\frac{3\mathrm{\pi }}{2},-\frac{\mathrm{\pi }}{2}\right)\cup \left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)\cup \left(\frac{\mathrm{\pi }}{2},\frac{3\mathrm{\pi }}{2}\right)$ is equal to