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=\…

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

[JEE Main 2023, 10 Apr (Shift 2)]