\[\frac{{{\pi ^2}}}{3} = 3 + \frac{1}{{\frac{2}{1} + \frac{2}{2} + \frac{1}{{\frac{2}{2} + \frac{2}{3} + \frac{1}{{\frac{2}{3} + \frac{2}{4} + \frac{1}{{\frac{2}{4} + \frac{2}{5} + \frac{1}{{...}}}}}}}}}}\]