The line of shortest distance between the lines \(\displaystyle \frac{x-2}{0} = \frac{y-1}{1} = \frac{z}{1} \) and \(\displaystyle \frac{x-3}{2} = \frac{y-5}{2} = \frac{z-1}{1} \) makes an angle of \(\displaystyle \cos^{-1}\!\left(\sqrt{\frac{2}{27}}\right) \) with the plane \( P: ax - y - z = 0, \ (a>0) \). If the image of the point \( (1,1,-5) \) in the plane \( P \) is \( (\alpha,\beta,\gamma) \), then \( \alpha + \beta - \gamma \) is equal to ______.
