GATE Electronics and Communications (EC) 2017 Shift 1 Solved Paper

Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by
$\mathit{h}\left[0\right]=\frac{1}{3};\mathit{h}\left[1\right]=\frac{1}{3};\mathit{h}\left[2\right]=\frac{1}{3};$  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(ω₀) = 0 and 0 < ω₀ < π, the value of ω₀ (in radians) is equal to ________.