3．
\(6\)、\((\)本小题满分\(12\)分\()\)已知等比数列\(\{{{a}_{n}}\}\)的前\(n\)项和为\({{S}_{n}},{{a}_{n}} > 0,{{a}_{1}}=\dfrac{2}{3}\)，且\(-\dfrac{3}{{{a}_{2}}},\dfrac{1}{{{a}_{3}}},\dfrac{1}{{{a}_{4}}}\)成等差数列．
\((I)\)求数列\(\{{{a}_{n}}\}\)的通项公式；
\((II)\)设数列\(\{{{b}_{n}}\}\)满足\({{b}_{n}}\cdot {{\log }_{3}}(1-{{S}_{n+1}})=1\)，求适合方程\({{b}_{1}}{{b}_{2}}+{{b}_{2}}{{b}_{3}}+...+{{b}_{n}}{{b}_{n+1}}=\dfrac{25}{51}\)的正整数\(n\)的值．