JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 21

Let S = {θ ∈ (0, 2π) : $7\cos^2\theta-3\sin^2\theta-2\cos^22\theta=2$}. Then, the sum of roots of all the equations $x^2-2(\tan^2\theta+\cot^2\theta)x+6\sin^2\theta=0$, θ ∈ S, is _______.