# Hello 2016

Geometry Level 3

For real numbers $$a,b,c,d$$ and $$e$$, we are given that $$\sin^{-1}a + \sin^{-1}b + \sin^{-1}c + \sin^{-1}d + \sin^{-1}e = \dfrac{5\pi}2$$.

For real $$x$$, let $$f$$ denote the maximum value of $$3\sin x + 4\cos x$$ and $$g$$ denote the minimum positive value of $$\tan x + \dfrac1{\tan x}$$.

Compute $$\dfrac{a^{2016} + b^{2016} + c^{2016} + d^{2016} + e^{2016} + 5g}{abcdef}$$.

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