如图\(1\),四边形\(ABCD\)为正方形,延长\(DC\)至\(E\),使得\(CE=2DC\),将四边形\(ABCD\)沿\(BC\)折起到\(A_{1}BCD_{1}\)的位置,使平面\(A_{1}BCD_{1}⊥\)平面\(BCE\),如图\(2\).
\((I)\)求证:\(CE⊥\)平面\(A_{1}BCD_{1}\);
\((II)\)求异面直线\(BD_{1}\)与\(A_{1}E\)所成角的大小;
\((III)\)求平面\(BCE\)与平面\(A_{1}ED_{1}\)所成锐二面角的余弦值.