Leaflet map not displayed properly inside tabbed panel

I'm trying to use Leaflet.js to display a map inside a tabbed panel from Twitter Bootstrap, but is behaving in a strange way:

When I click on the tab containing the panel there is a gray layer on top of the map. If I drag and move the map I get to see other tiles, but not the initial ones.

Even more strange is that if I resize the browser, suddenly it works perfectly, until I reload again, so I would guess is a problem with the css, but I cannot find the problem.

Also, placing the map outside of the tabbed panel works great.

I tested in Firefox and Chrome, and both have the same issue.

I created a test in jsfiddle to see it "live": http://jsfiddle.net/jasalguero/C7Rp8/1/

Any help is really appreciated!

It's a complete hack from messing with the leaflet.js source code, but it works (at least in jsFiddle) http://jsfiddle.net/C7Rp8/4/

The idea is from Google Maps, to "resize" or "redraw" the map when its container div is resized.

The changes I made are:

add id link3 to the small tab in HTML

<a href="#lC" data-toggle="tab" id="link3">tab3</a>

add a listener to this tab inside $(function() {

$("body").on('shown','#link3', function() { 
  L.Util.requestAnimFrame(map.invalidateSize,map,!1,map._container);
});

The requestAniMFrame line is taken from trackResize in leaflet.js

Update from the comments: Hi, I used map.invalidateSize(false); instead of L.Util.requestAnimFrame(... and this also seems to work. Just thought I'd point this out. Great answer though! – Herr Grumps

Bootstrap 3 has custom namespaced events, and so previous answers would work with:

$("body").on("shown.bs.tab", "#link3", function() {
    map.invalidateSize(false);
});

Reference: Bootstrap Tabs