Answer
$ -\frac{1}{4} $
Work Step by Step
$3cos^{-1}(2x)=2\pi \Longrightarrow cos^{-1}(2x)=\frac{2\pi}{3} \Longrightarrow 2x=cos\frac{2\pi}{3}=-\frac{1}{2} \Longrightarrow x=-\frac{1}{4} $
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