There are a few other ways.
You could include a small
applet on the page which reads the time from the browser and sends it direct to the server.
What most time-sensitive applications do, though is to use a cookie containing a time offset from server time. Typically the web application might try to read the cookie on each communication from a client browser - if the cookie is absent, redirect to a "whast time is it?" page, then set the cookie based on the answer before forwarding to the real destination page. Much like login, really.
A combination of the two approaches above would look for the cookie, if the cookie is not found, send a page containing a small applet which sends back the client time, then the web app sets the cookie based on the message from the applet. Almost magic, and no URL-rewriting or JavaScript needed!