$(7 : \frac{5}{6} - 8\frac{1}{9}) * 2\frac{2}{5} : ((\frac{3}{8} + \frac{5}{6} + \frac{5}{12}) * \frac{8}{25}) = (7 * \frac{6}{5} - \frac{73}{9}) * \frac{12}{5} : ((\frac{3}{8} + \frac{5}{6} + \frac{5}{12}) * \frac{8}{25}) = (\frac{42}{5} - \frac{73}{9}) * \frac{12}{5} : (\frac{3 * 3 + 5 * 4 + 5 * 2}{24} * \frac{8}{25}) = (8\frac{2}{5} - 8\frac{1}{9}) * \frac{12}{5} : (\frac{9 + 20 + 10}{24} * \frac{8}{25}) = (\frac{2}{5} - \frac{1}{9}) * \frac{12}{5} : (\frac{39}{24} * \frac{8}{25}) = \frac{2 * 9 - 1 * 5}{45} * \frac{12}{5} : (\frac{39}{24} * \frac{8}{25}) = \frac{18 - 5}{45} * \frac{12}{5} : \frac{39 * 8}{24 * 25} = \frac{13}{5 * 3 * 3} * \frac{4 * 3}{5} * \frac{24 * 5 * 5}{13 * 3 * 4 * 2} = \frac{1}{3} * 4 = \frac{4}{3} = 1\frac{1}{3}$