Let P={θ ∈[0,4 π]: tan^2 θ ≠ 1} and S={a ∈ Z: 2( cos^8 θ- sin^8 θ) sec 2 θ=a^2, θ ∈ P}. Then n(S) is:

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