Let $\mathrm{S}=\left\{\mathrm{\theta }\in [0,2\mathrm{\pi }]:8^{2{\sin }^2\mathrm{\theta }}+8^{2{\cos }^2\mathrm{\theta }}=16\right\}$ then $\mathrm{n}\left(\mathrm{S}\right)+\sum _{\mathrm{\theta }\in \mathrm{S}} \left(\sec \left(\frac{\mathrm{\pi }}{4}+2\mathrm{\theta }\right)\mathrm{cosec}\left(\frac{\mathrm{\pi }}{4}+2\mathrm{\theta }\right)\right)$ is 

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