Does my cat have XXY sex chromosomes?

My orange cat has a patch of dark brown fur on his nose. Does he have XXY genes since he has two colors? Here is a picture of looking uncomfortable in his Halloween costume:

https://sphotos-b.xx.fbcdn.net/hphotos-ash4/406554_10150574630822830_1514038057_n.jpg

(I am a long time lurker, first time poster on reddit, if there is a better subreddit for this question I would be much obliged to know).