答案是4sqrt(3)/9.
sin(A)sin(2A)=2sin^2(A)cos(A)=2(1-cos^2A)cos(A).
设cos(A)=x,则所求式子即为
f(x)=2(1-x^2)x.
易求f'(x)=2(1-3x^2). 令f'=0可解出x=+-1/sqrt(3),它们都在定义域-1