x∈[π/4,3π/4]
2x+π/6∈[2π/3,5π/3]
所以sin（2x+π/6）∈[-1,根号3/2]
所以-2asin（2x+π/6）∈[-a根号3,2a]
所以f(x)∈[2a-根号3a+b,4a+b]
所以2a-根号3a+b=-3,4a+b=根号3-1
解得a=1 ,b=根号3-5