In your code, filter apply on 'items' array, not on each array item, that's why it does not work as you expect.
Instead, you can use ng-show (or ng-if):
<ul>
<li ng-repeat="item in items" ng-show="$index % 3 == 0">{{item}}</li>
</ul>
See: http://jsfiddle.net/H7d26
EDIT: Use ng-if directive if you do not want to add invisible dom elements:
<ul>
<li ng-repeat="item in items" ng-if="$index % 3 == 0">{{item}}</li>
</ul>
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