Mark M. answered 02/25/16
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Retired math prof. Very extensive Precalculus tutoring experience.
Tan(cos-1(-1/4)) = Tanθ, where θ = cos-1(-1/4)
cosθ = -1/4 and π/2 < θ < π
Tan(cos-1(-1/4)) = Tanθ = -√15