\(\Rightarrow-\pi< \frac{\pi}{3}-a< -\frac{\pi}{2}\Rightarrow sin\left(\frac{\pi}{3}-a\right)< 0\)
\(\Rightarrow sin\left(\frac{\pi}{3}-a\right)=-\sqrt{1-cos^2\left(\frac{\pi}{3}-a\right)}=-\frac{\sqrt{21}}{5}\)
\(\left\{{}\begin{matrix}cos\left(\frac{\pi}{3}-a\right)=-\frac{2}{5}\\sin\left(\frac{\pi}{3}-a\right)=-\frac{\sqrt{21}}{5}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\frac{1}{2}cosa+\frac{\sqrt{3}}{2}sina=-\frac{2}{5}\\\frac{\sqrt{3}}{2}cosa-\frac{1}{2}sina=-\frac{\sqrt{21}}{5}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-\frac{\sqrt{3}}{2}cosa-\frac{3}{2}sina=\frac{2\sqrt{3}}{5}\\\frac{\sqrt{3}}{2}cosa-\frac{1}{2}sina=-\frac{\sqrt{21}}{5}\end{matrix}\right.\)
Cộng vế với vế: \(-2sina=\frac{2\sqrt{3}-\sqrt{21}}{5}\Rightarrow sina=\frac{\sqrt{21}-2\sqrt{3}}{10}\)
