The year in question .....

Geometry Level 4

It is the case that S=n=12015csc((2n+4))=sec(k)S = \displaystyle\sum_{n=-1}^{2015} \csc((2^{n+4})^{\circ}) = \sec(k^{\circ}) for some integer 0<k<900 \lt k \lt 90. Find kk.

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