Usability: Webinar timings

Here is an image from a GoToMeeting's webinar page. I've logged into the webinar and it tells me to come back at another time.

Here is the problem:

Now I have to go to a timezone page and figure out the local time when this event is happening. And if daylight savings is involved there is a really good chance that I'll be off by 1 hour end end up missing the event.

This is not just an issue with GoToMeeting. I've seen it time and again with most webinar providers. And I've missed my fair share of webinars because of messing up the conversion (especially with daylight savings involved!!).

Why does it tell me the time in the PDT timezone? Why can't it use javascript on the browser to convert the time into my local timezone?

Or, at least have a message like "This webinar starts in 12 hours, 45 minutes". That way I get a fairly good idea of when it's going to happen.