\[\frac{{2{\pi ^2}}}{3} = 7 - \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{\frac{2}{2} + \frac{1}{{\frac{2}{2} + \frac{1}{{\frac{2}{3} + \frac{1}{{\frac{2}{3} + ...}}}}}}}}}}}} = 7 - \left[ {0;2,2,\frac{2}{2},\frac{2}{2},\frac{2}{3},\frac{2}{3},\frac{2}{4},\frac{2}{4},\frac{2}{5},\frac{2}{5}...} \right].\]