How would I use AngularJS ng-repeat to repeat this structure

If you're iterating over an array of items and need alternating black/white backgrounds then you can do it like this:

<div ng-repeat="item in items" ng-class-odd="'black'" ng-class-even="'white'">
</div>

http://jsfiddle.net/fNCnr/1/

<div ng-repeat="color in ['black','white']" class="{{color}}"></div>

Output:

<div ng-repeat="color in ['black','white']" class="black"></div>
<div ng-repeat="color in ['black','white']" class="white"></div>

Or (more verbose):

<div ng-repeat="color in ['black','white']" ng-class="color"></div>

Output:

<div ng-repeat="color in ['black','white']" ng-class="color" class="ng-scope black"></div>
<div ng-repeat="color in ['black','white']" ng-class="color" class="ng-scope white"></div>

In your controller you define a list of colors:

$scope.colors = ['black', 'white', 'black', 'white', 'black', 'white', ...];

Html:

<div ng-repeat="color in colors" ng-class="color"></div>

See jsFiddle.