如图，在斜三棱柱\(ABC-A _{1} B _{1} C _{1}\)中，点\(O\)、\(E\)分别是\(A _{1} C _{1}\)、\(A _{1} B _{1}\)的中点，\(A _{1} C\)与\(AC _{1}\)交于点\(F\)，\(AO⊥\)平面\(A _{1} B _{1} C _{1} .\)已知\(∠BCA=90°\)，\(AA _{1} =AC=BC=2\)．
\((1)\)求证：\(EF/\!/\)平面\(BB _{1} C _{1} C\)；
\((2)\)求\(A _{1} C _{1}\)与平面\(AA _{1} B _{1}\)所成角的正弦值．