$2sin^23x=1$
$↔ sin^23x=\dfrac{1}{2}$
$↔ \left[ \begin{array}{l}sin3x=\dfrac{\sqrt[]{2}}{2}\\sin3x=-\dfrac{\sqrt[]{2}}{2}\end{array} \right.$
$↔ \left[ \begin{array}{l}3x=\dfrac{\pi}{4}+k2\pi\\3x=-\dfrac{\pi}{4}+k2\pi\\3x=\dfrac{3\pi}{4}+k2\pi\\3x=\dfrac{5\pi}{4}+k2\pi\end{array}\\ \right.$
$↔ \left[ \begin{array}{l}x=\dfrac{\pi}{12}+k\dfrac{2\pi}{3}\\x=-\dfrac{\pi}{12}+k\dfrac{2\pi}{3}\\x=\dfrac{\pi}{4}+k\dfrac{2\pi}{3}\\x=\dfrac{5\pi}{12}+k\dfrac{2\pi}{3}\end{array}\\ \right.$ $(k∈\mathbb{Z})$
Kết hợp nghiệm ta được: $x=\dfrac{\pi}{12}+k\dfrac{\pi}{6}$
Vậy $\left\{ \begin{array}{l}a=1\\b=12\end{array} \right.$ $→ a+b=13$
