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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