For $\mathrm{x}\in (0,\mathrm{\pi })$ the equation $\sin \mathrm{x}+2\sin 2\mathrm{x}-\sin 3\mathrm{x}=3$ has

$\begin{array}{l}\sin \mathrm{x}+2\sin 2\mathrm{x}-\sin 3\mathrm{x}=3\\ \sin \mathrm{x}\left(1+4\cos \mathrm{x}-3+4{\sin }^2 \mathrm{x}\right)=3\\ 3-4{\left(\cos \mathrm{x}-\frac{1}{2}\right)}^2=\frac{3}{\sin \mathrm{x}}\\ 4{\sin }^2 \mathrm{x}\end{array}$
$\begin{array}{l}4-4{\mathrm{c}}^2+4\mathrm{c}-2\\ 3-\left[4{\mathrm{c}}^2-4\mathrm{c}+1\right]\\ 3-(2\mathrm{c}-1{)}^2=\frac{3}{5}\end{array}$
L.H.S $\le$ 3; R.H.S $\ge$3, No Solution