Let h[n] be the impulse response of a discrete-time linear time invariant(LTI) filter. The impulse response is given by

$h[0]=\frac{1}{3};\,h[1]=\frac{1}{3};\,h[2]=\frac{1}{3}$; and $h[n]=0$ for $n<0$ and $n>2$.

Let $H(ω)$ be the discrete-time Fourier transform (DTFT) of $h[n]$, where $ω$ is the normalized angular frequency in radians. Given that $H(ω_{0})=0$ and $0< ω_{0}<π$, the value of $ω_{0}$ (in radians) is equal to__________.