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 \( …

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)]