Question Number 198062 by NANIGOPAL last updated on 09/Oct/23
Commented by mr W last updated on 10/Oct/23
$${equality}\:−\mathrm{2}\:{can}\:{not}\:{hold}! \\ $$$${equality}\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}\:{holds}\:{at}\:{A}={B}=\mathrm{20}°,\:{C}=\mathrm{140}°. \\ $$$$−\mathrm{2}<\mathrm{sin}\:\mathrm{3}{A}+\mathrm{sin}\:\mathrm{3}{B}+\mathrm{sin}\:\mathrm{3}{C}\leqslant\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$