Zimbra uses MySql database and when you try to connect to mysql under zimbra user with following details, it might throw access errors.
user : zimbra
password : [no password]
host: localhost ( or wherever you have installed the zimbra)
Also , if you already have your own mysql installed before , it might conflict for the mysql clients like CocoaMySQL. To make it work you need to specify the right socket path. Specify
/opt/zimbra/db/mysql.sock.
Once you specify above socket it exactly knows what mysql db to connect to. You can make this work for phpMyAdmin or any other MySQL clients.