Let S={θ ∈(0,2 π): 7 cos^2 θ-3 sin^2 θ-2 cos^2 2 θ=2}. Then, the sum of roots of all the equations x^2-2( tan^2 θ+ cot^2 θ) x+6 sin^2 θ=0, θ ∈ S, is…

Let $\displaystyle S=\left\{\theta \in(0,2 \pi): 7 \cos ^2 \theta-3 \sin ^2 \theta-2 \cos ^2 2 \theta=2\right\}$. Then, the sum of roots of all the equations $\displaystyle x^2-2\left(\tan ^2 \theta+\cot ^2 \theta\right) x+6 \sin ^2 \theta=0, \theta \in \mathrm{~S}$, is \_\_\_\_.