\(sina-cosa=\dfrac{1}{3}\left(0< a< \dfrac{\pi}{4}\right)\)
\(\Leftrightarrow\left(sina-cosa\right)^2=\dfrac{1}{9}\)
\(\Leftrightarrow sin^2a+cos^2a-2sinacosa=\dfrac{1}{9}\)
\(\Leftrightarrow1-sin2a=\dfrac{1}{9}\)
\(\Leftrightarrow sin2a=1-\dfrac{1}{9}=\dfrac{8}{9}\)