I got the same problem, and the solution is very simple: don't start a new line! Although some of the previous answers can solve the problem, the idea is not stated clearly. The important understanding is, to get rid of the unintended spaces, never start a new line just after your start tag.
The following way is WRONG and will leave a lot of unwanted spaces before your text content:
<textarea>
text content // start with a new line will leave a lot of unwanted spaces
</textarea>
The RIGHT WAY to do it is:
<textarea>text content //put text content right after your start tag, no new line
</textarea>