How can I find this all pass filter's phase?
phase of a filter is the angle (or "argument") of the complex number that is $H(e^{j\omega})$ at each value of $\omega$ .  you may need to "unwrap" the phase by adding or subtracting integer multiples of $2 \pi$ .

BTW, to post math to these pages, surround the $\LaTeX$ expression with single dollar signs for inline math and double dollar signs for math expressions on their own line.  if you need a quick guide for LaTeX, my suggestion is the one that lives at Wikipedia: https://en.wikipedia.org/wiki/Wikipedia:Math .  i'm still learning how to do other markup here.