Đáp án: 90
Giải thích các bước giải:
$\begin{array}{l}
{\left( {\sin 3x - \sqrt 3 cos3x} \right)^2} + 3\sin \left( {3x - \frac{\pi }{3}} \right) = 7\\
\Rightarrow {\left( {\frac{1}{2}\sin 3x - \frac{{\sqrt 3 }}{2}\cos 3x} \right)^2} + \frac{3}{4}\sin \left( {3x - \frac{\pi }{3}} \right) - \frac{7}{4} = 0\\
\Rightarrow {\left( {\sin \frac{\pi }{3}.\sin 3x - \cos \frac{\pi }{3}.\cos 3x} \right)^2} + \frac{3}{4}\sin \left( {3x - \frac{\pi }{3}} \right) - \frac{7}{4} = 0\\
\Rightarrow {\sin ^2}\left( {3x - \frac{\pi }{3}} \right) + \frac{3}{4}\sin \left( {3x - \frac{\pi }{3}} \right) - \frac{7}{4} = 0\\
\Rightarrow \left[ \begin{array}{l}
\sin \left( {3x - \frac{\pi }{3}} \right) = 1\\
\sin \left( {3x - \frac{\pi }{3}} \right) = - \frac{7}{4}\left( {ktm} \right)
\end{array} \right.\\
\Rightarrow \left( {3x - \frac{\pi }{3}} \right) = \frac{\pi }{2} + k2\pi \\
\Rightarrow x = \frac{{5\pi }}{{18}} + \frac{{k2\pi }}{3}\\
\Rightarrow \frac{{a\pi }}{b} = \frac{{5\pi }}{{18}}\\
\Rightarrow a.b = 5.18 = 90
\end{array}$
