Let \(P=\left{\theta \in [0,4\pi ]:{\tan }^{2}\theta \neq 1\right}\) and \(S=\left{a\in Z:2\left({\cos }^{8}\theta -{\si…

Let \(P=\left{\theta \in [0,4\pi ]:{\tan }^{2}\theta \neq 1\right}\) and \(S=\left{a\in Z:2\left({\cos }^{8}\theta -{\sin }^{8}\theta \right)\right.\left.\sec 2\theta ={a}^{2},\theta \in P\right}\). Then \(n(S)\) is:

[JEE Main 2026, 2 Apr (Shift 2)]