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 -{…

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)]