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已知点\(O\)为坐标原点，点\(A_{n}(n, \dfrac {1}{n+2})(n∈N^{*})\)，向量\( \overrightarrow{i}=(0,1)\)，\(θ_{n}\)是向量\( \overrightarrow{OA_{n}}\)与\(i\)的夹角，则使得\( \dfrac {\cos θ_{1}}{\sin \theta _{1}}+ \dfrac {\cos θ_{2}}{\sin \theta _{2}}+ \dfrac {\cos θ_{3}}{\sin \theta _{3}}+…+ \dfrac {\cos θ_{n}}{\sin \theta _{n}} < t\)恒成立的实数\(t\)的最小值为\((\) \()\)