A New Function

Geometry Level 3

Let \(ArcTrig(x)=\sin^{-1}\frac{1}{x}+\cos^{-1}\frac{1}{x}+\tan^{-1}x+\csc^{-1}x+\sec^{-1}x+\cot^{-1}x.\) What is \(ArcTrig\left(\frac{4}{\sqrt{5}+1}\right)\) in degrees?

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