Question Number 217894 by hardmath last updated on 23/Mar/25
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{holds}: \\ $$$$\Sigma\:\frac{\mathrm{cot}\:\mathrm{A}}{\:\sqrt{\mathrm{cot}\:\mathrm{B}\:\:+\:\:\mathrm{3}\:\mathrm{cot}\:\mathrm{C}}}\:\:\geqslant\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\sqrt[{\mathrm{4}}]{\mathrm{27}}\: \\ $$