x∈[0,π/2]时,x2/π≤sinx≤x,所以A=2/π,B=1.
(B-A)min=1-2/π.
(sinA+sinB+sinC)/3≥sin[(A+B+C)/3]
所以sinA+sinB+sinC≥3sin(π/3)=3√3/2.
M的最大值为3√3/2.