The angle at which the line, $\frac{x-1}{0}=\frac{2-y}{-1}=\frac{2z-3}{-2}$ is inclined with the positive direction of z-axis is

$\frac{3\pi}{4}$

$\frac{x-1}{0} = \frac{2-y}{-1} = \frac{2z-3}{-2} = \lambda$

$x = 1$

$2 - y = -\lambda \Rightarrow y = 2 + \lambda$

$2z - 3 = -2\lambda \Rightarrow z = \frac{3}{2} - \lambda$

$\text{Direction ratios} = (0,1,-1)$

$\text{Direction cosines: } l = 0,\; m = \frac{1}{\sqrt{2}},\; n = \frac{-1}{\sqrt{2}}$

$\cos\theta = n = \frac{-1}{\sqrt{2}}$

$\theta = \cos^{-1}\left(\frac{-1}{\sqrt{2}}\right) = \frac{3\pi}{4}$

Final Answer: $\frac{3\pi}{4}$