[tex]$\sin x\neq 0\Rightarrow \frac{2\sin^2x+3\cos x-3}{\sin x}=0\Leftrightarrow 2\sin^2x+3\cos x-3=0$[/tex]

[tex]$2\left ( 1-\cos^2x \right )+3\cos x-3=0\Leftrightarrow 2-2\cos^2x+3 \cos x-3=0$[/tex]

[tex]$-2\cos^2x +3\cos x-1=0\Leftrightarrow 2\cos ^2x-3\cos x+1=0$[/tex]

[tex]$\left ( \cos x-1 \right )\left ( 2\cos x-1 \right )=0\Rightarrow x=\left \{ 2\pi k ,\pm \frac{\pi}{3}+2\pi k \right \},k\in \mathbb{Z}$[/tex]

[tex]$x\in [0,4\pi]\Rightarrow k=\left \{ 0,1,2 \right \}\Rightarrow x=\left \{ \frac{\pi}{3},\frac{5\pi}{3},\frac{7\pi}{3} ,\frac{11\pi}{3}\right \}=\left \{ 60^{\circ},300^{\circ},420^{\circ},660^{\circ} \right \}$[/tex]

Сумма корней: [tex]1440^{\circ}[/tex]