(2007•海淀区一模)已知正四棱柱ABCD-A1B1C1D1中,AB=2,AA1=3.
(Ⅰ)求证:A1C⊥BD;
(Ⅱ)求直线A1C与侧面BB1C1C所成的角的正切值;
(Ⅲ)求二面角B1-CD-B的正切值.