Let $z_1$ and $z_2$ be two complex numbers such that arg $\left(z_1-z_2\right)=\frac{\pi}{4}$ and $z_1, z_2$ satisfy the equation $|z-3|=$
$\operatorname{Re}(z)$. Then the imaginary part of $z_1+z_2$ is equal to $\_\_\_\_$ .
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