Deque implemented using a circular array
I do not see any problems with addCount as long as we add a disclaimer that this solution is not thread safe.

The presented solution is a collection that can only accept int items. You can expand this if you add generic parameter to the class. Note that in this case, the internal array is of Object[] type and you let the compiler enforce type safety and also do auto-boxing to support primitive data items, just like in Java collections library. And while we mentioned that, you might want to consider making your solution implement the Deque interface from Java collections so that clients will work with a familiar API (of course you will want to change the name of the class to reflect that it is a concrete implementation of a Deque)