已知在正四棱柱\(ABCD-A _{1} B _{1} C _{1} D _{1}\)中，\(AB=2\)，二面角\(C _{1} -AB-C\)的大小为\(60°\)，点\(F\)为棱\(DD _{1}\)的中点，点\(E\)在核\(BB _{1}\)上，且\(BE= \dfrac {1}{4} BB _{1}\)．
\((\)Ⅰ\()\)在图\(1\)中，过\(A\)，\(E\)，\(F\)三点作正四棱柱\(ABCD-A _{1} B _{1} C _{1} D _{1}\)的截面，并指出截面和棱\(C _{1} C\)交点\(G\)的位置\((\)不必说明画法和理由\()\)；
\((\)Ⅱ\()\)求直线\(A _{1} B\)和平面\(BB _{1} D _{1} D\)所成角的余弦值\((\)如图\(2)\)；
\((\)Ⅲ\()\)求四面体\(A _{1} EBF\)的体积\((\)如图\(2)\)．