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Solve:

$\mathrm{arccot}\left(\tan\frac{4\pi}{5}\right)$

$\mathrm{arccot}\left(\tan\frac{4\pi}{5}\right)=\mathrm{arccot}\left(\frac{1}{\cot\frac{4\pi}{5}}\right)\\\frac{1}{\cot\frac{4\pi}{5}}=\alpha$

at the moment I don't know what to do

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Let $x=\operatorname{arccot}(\tan y)$; then, by definition, $\cot x=\tan y$, so $\cot x=\cot(\pi/2-y)$ and therefore $$ x=\frac{\pi}{2}-y+k\pi $$ with the integer $k$ chosen so that $0<x<\pi$ (the range of the cotangent function).

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