(Ⅰ)在三角形AGM中,由正弦定理：
sin∠AMG/AG=sin∠MAG/GM
其中∠MAG=30°,
∠AMG=180°-(30°+α),
AG=2/3*AD=2/3*sin60°*AB=根号3/3,
GM=sin∠MAG*AG/sin∠AMG=根号3/6sin(30°+α)
同理,在三角形AGN中,
GN=根号3/6sin(a-30°)
S1=1/2AG·GMsinα=1/2*根号3/3*根号3/6sin(30°+α)*sinα=sinαsin(30°+α)/12
S2=1/2AG·GNsin(180°-α)=1/2*根号3/3*根号3/6sin(a-30°)*sinα=sinαsin(a-30°)/12
(Ⅱ)y=1/(S1^2)+ 1/(S2^2)
=144/[(sinα)^2*sin^2(a-30°)]+144/[(sinα)^2*sin^2(30°+α]
=72(3+cot^2α)
∵π/3