You can also do this:
B=π/3
A+C=2π/3
sinA sinc = sinA sin(2π/3-A)= sinA(√3/2 cosa+ 1/2 sinA)
=√3/4 sin2a- 1/4 cos 2a+ 1/4
= 1/2(√3/2 sin2a- 1/2 cos 2a)+ 1/4
= 1/2 octyl (2A-π/6)+ 1/4
0 & ltA & lt2π/3
-π/6 & lt； 2A-π/6 & lt； 7π/6
The range of sinAsinC is: (0,3/4)
SinAsinC max =3/4