已知三棱锥\(P-ABC(\)如图\(1)\)的平面展开图\((\)如图\(2)\)中,四边形\(ABCD\)为边长为\( \sqrt {2}\)的正方形,\(\triangle ABE\)和\(\triangle BCF\)均为正三角形,在三棱锥\(P-ABC\)中:
\((I)\)证明:平面\(PAC⊥\)平面\(ABC\);
\((\)Ⅱ\()\)求二面角\(A-PC-B\)的余弦值;
\((\)Ⅲ\()\)若点\(M\)在棱\(PC\)上,满足\( \dfrac {CM}{PM}=λ\),\(λ∈[ \dfrac {1}{3}, \dfrac {2}{3}]\),点\(N\)在棱\(BP\)上,且\(BM⊥AN\),求\( \dfrac {BN}{BP}\)的取值范围.