Trigonometric Functions And Equations

Let \(S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^{2} x}+9^{\tan ^{2} x}=10\right\}\) and

\(\beta=\sum_\limits{x \in S} \tan ^{2}\left(\frac{x}{3}\right)\), then \(\frac{1}{6}(\beta-14)^{2}\) is equal to :