（1）解析：∵f(x)=Asin(wx+φ)(A>0,w>0,| φ|T=2π==>w=2π/T=1
∴f(x)=2sin(x+φ)==> f(5π/6)=2sin(5π/6+φ)=2==>5π/6+φ=π/2==>φ=-π/3
∴f(x)=2sin(x-π/3)
(2)解析：设g(x)=f(2x+π/3)+f^2(x+π/3)>0
g(x)=2sin(2x)+4sin^2(x)=2(sin(2x)-cos2x)+2=2√2sin(2x-π/4)+2
(文)√2sin(2x-π/4)+1>0==> sin(2x-π/4)> -1/√2
2kπ