如图\((1)\),五边形\(ABCDE\)中,\(ED=EA\),\(AB/\!/CD\),\(CD=2AB\),\(∠EDC=150^{\circ}.\)如图\((2)\),将\(\triangle EAD\)沿\(AD\)折到\(\triangle PAD\)的位置,得到四棱锥\(P-ABCD.\)点\(M\)为线段\(PC\)的中点,且\(BM⊥\)平面\(PCD\).
\((1)\)求证:平面\(PAD⊥\)平面\(PCD\);
\((2)\)若直线\(PC\)与\(AB\)所成角的正切值为\( \dfrac {1}{2}\),设\(AB=1\),求四棱锥\(P-ABCD\)的体积.