How do I tab off a textarea in a Java application?

Question

At work I am obliged to use a proprietary Java Web Start application for filling in certain forms. I suspect that the application uses Swing as its widget toolkit.

I prefer to fill in the forms using the keyboard because it's much faster that way. Usually I can press the Tab key to cycle focus through the input fields. However, this doesn't work with multi-line textarea fields, where Tab inputs a literal tab. I can't find any way of using the keyboard to move focus off these textarea fields.

Is there a default key combination in Swing that shifts focus off of a textarea field?