Trigonometry · Trigonometric identities and range

Let

P = \{\theta \in [0, 4\pi] : \tan^2\theta \neq 1\}

and

S = \{a \in \mathbb{Z} : 2(\cos^8\theta - \sin^8\theta)\sec2\theta = a^2,\ \theta \in P\}.

Then

n(S)

is:

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