$\begin{gathered}
\frac{{\sqrt 2 \sin \left( {x + \frac{\pi }{4}} \right)}}{{\sqrt 2 cos3x}} = \left( { - 8{{\sin }^2}x + 6} \right)\sin x = 2\left( {3\sin x - 4{{\sin }^3}x} \right) \hfill \\
\sin \left( {x + \frac{\pi }{4}} \right) = 2\sin 3xcos3x = \sin 6x \hfill \\
6x = 2k\pi + x + \frac{\pi }{4} \to x = \frac{{\left( {8k + 1} \right)\pi }}{{20}} \hfill \\
6x = 2k\pi + \pi - x - \frac{\pi }{4} \to x = \frac{{\left( {8k + 3} \right)\pi }}{{28}} \hfill \\
a + b + c = 8 + (1 + 3) + (20 + 28) = 60 \hfill \\
\end{gathered} $