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Geometry Level 2

1cos2(a)+11+sin2(a)+21+sin4(a)+41+sin8(a)\large \frac1{\cos^2(a)} + \frac1{1+\sin^2(a)} + \frac2{1+\sin^4(a) } +\frac4{1+\sin^8(a)}

If sin16(a)=15 \sin^{16} (a) = \frac15, evaluate the expression above.

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