\(\frac{10}{7}\cdot\frac{2}{3}+\frac{5}{6}:\frac{3}{10}-\frac{2}{3}\cdot\frac{3}{7}\)
\(=\left(\frac{10}{7}\cdot\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{7}\right)+\frac{5}{6}\cdot\frac{10}{3}\)
\(=\frac{2}{3}\left(\frac{10}{7}-\frac{3}{7}\right)+\frac{5\cdot10}{6\cdot3}\)
\(=\frac{2}{3}\cdot1+\frac{25}{9}\)
\(=\frac{2}{3}+\frac{25}{9}\)
\(=\frac{31}{9}\)