\(y=sinx.sin\left(x-\dfrac{\pi}{6}\right)+3=\dfrac{1}{2}cos\left(\dfrac{\pi}{6}\right)-\dfrac{1}{2}cos\left(2x-\dfrac{\pi}{6}\right)+6\)
\(=6+\dfrac{\sqrt{3}}{4}-\dfrac{1}{2}cos\left(2x-\dfrac{\pi}{6}\right)\)
Do \(-1\le cos\left(2x-\dfrac{\pi}{6}\right)\le1\)
\(\Rightarrow\dfrac{22+\sqrt{3}}{4}\le y\le\dfrac{26+\sqrt{3}}{4}\)