f(x) 周期為 6
f(1)+f(2)+f(3)+f(4)+f(5)+f(6)
= sin π/3 + sin 2π/3 + sin π + sin 4π/3 + sin 5π/3 + sin 2π
= sin π/3 + sin 2π/3 + 0 + sin -2π/3 + sin -π/3 + 0
= sin π/3 + sin 2π/3 + 0 - sin 2π/3 - sin π/3 + 0
= 0.
所以
f(1)+f(2)+f(3)+.+f(2010), 【2010/6=335】
= 0+0+0+.+0+0
=0