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Geometry Level 4

\[s=\sec { \frac { 0\pi }{ 2016 } } \sin { \frac { \pi }{ 2016 } } \sec { \frac { 2\pi }{ 2016 } } +\sec { \frac { 2\pi }{ 2016 } } \sin { \frac { 3\pi }{ 2016 } } \sec { \frac { 4\pi }{ 2016 } } \\ +\ldots +\sec { \frac { 670\pi }{ 2016 } } \sin { \frac { 671\pi }{ 2016 } } \sec { \frac { 672\pi }{ 2016 } } \]

If \(s\) satisfy the equation above, find \(s\pi\).

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