Let S = $\left\{\theta \in \left[0,2\pi \right]:8^{2si{n}^2\theta }+8^{2co{s}^2\theta }=16\right\}.$ Then $n\left(S\right)+{\displaystyle \sum _{\theta \in S}^{}\left(sec\left(\frac{\pi }{4}+2\theta \right)cosec\left(\frac{\pi }{4}+2\theta \right)\right)}$ is equal to:

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