If $\mathrm{\theta }={\tan }^{-1}\left(2{\tan }^2\mathrm{\theta }\right)-\frac{1}{2}{\sin }^{-1}\left(\frac{3 \sin 2\mathrm{\theta }}{5+4 \cos 2\mathrm{\theta }}\right)$ then find the sum of all the possible values of tan θ.