Don't do this. Zimbra is a complicated beast with lot of components and it should run on a dedicated server or VM.
For the specific problem: Obviously, you noticed that there is a conflict between Zimbras own web server and the one you installed. If you insist to continue with this, you would have to change ports for the Zimbra web server installation and then configure a reverse proxy in Apache to forward requests, e.g. to
http://example.com/zimbra to the altered port of the Zimbra web server.
Again: Don't do this. There is also no need if you have another server as a web server. RT plays nicely with most web servers and it's easy to get the mail into it from another server - there is no need to put it on the same host as the mail server.