f(π/4)=2sin(2*π/4+π/3)=2sin5π/6
f(2π/4)=2sin(2*2π/4+π/3)=2sin4π/3
f(3π/4)=2sin(2*3π/4+π/3)=2sin11π/6
f(4π/4)=2sin(2π+π/3)=2sin7π/3=2sinπ/3
f(5π/4)=2sin(2*5π/4+π/3)=2sin17π/6=2sin5π/6
f（x)是四个一循环的函数
又因为f(π/4)+f(3π/4)=0 f(2π/4)+f(4π/4)=0
f（x)=2sin(2x+π/3),求f(π/4)+f(2π/4)+f(3π/4)+……+f(2013π/4)=f(2013π/4)=2sin5π/6=1