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已知直三棱柱\(ABC-A_{1}B_{1}C_{1}\)中,\(∠CAB=∠CBA= \dfrac {π}{4},CC_{1}=AB, \overrightarrow{AA_{1}}=4 \overrightarrow{AE}, \overrightarrow{A_{1}F}= \dfrac {3}{8} \overrightarrow{A_{1}B_{1}}, \overrightarrow{AG}= \overrightarrow{GB}\),点\(H\)在线段\(EG\)上.
\((1)\)证明:\(EF⊥CH\);
\((2)\)求平面\(BCC_{1}B_{1}\)与平面\(CEF\)所成锐二面角的余弦值.