π/4≤x≤3π/4,
π/2≤2x≤3π/2,
2π/3≤2x+π/6≤5π/3,
-2≤2sin(2x+π/6)≤√3,
-2≤f(x)≤√3.
a>0
b≤F(x)≤√3a+2a+b
b=-√3,
√3a+2a+b=(√3)-1,
a=(2(√3)-1)/(√3+2)>0,
ab=(√3-6)/(√3+2).
a