平面\(a\)过正方体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)的顶点\(A\)，\(a/\!/\)平面\(CB_{1}D_{1}\)，\(a∩ \)平面\(ABCD=m\)，\(a∩ \)平面\(ABA_{1}B_{1}=n\)，则\(m\)，\(n\)所成角的正弦值为\((\) \()\)
A. \(\dfrac{ \sqrt{3}}{2} \)
B. \(\dfrac{ \sqrt{2}}{2} \) C. \(\dfrac{ \sqrt{3}}{3} \) D. \(\dfrac{1}{3} \)
