Let tan A, tan B, where A, B ∈(-(π)/2, (π)/2), be the roots of the quadratic equation x^2-2 x-5=0. Then 20 sin^2((A + B)/2) is equal to:

Let $\displaystyle \tan A, \tan B$, where $\displaystyle A, B \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, be the roots of the quadratic equation $\displaystyle x^2-2 x-5=0$. Then $\displaystyle 20 \sin ^2\left(\frac{\mathrm{~A}+\mathrm{B}}{2}\right)$ is equal to: