He has cheated and lied twice now... how many more times are you willing to take a chance on? As was said, when he is gone, he will have ample opportunity to continue and you would never know about it... and he certainly wouldn't tell you about it if he did, or even be honest about it if you were to ask!
He will be around a good number of single guys who will want to go out and have a good time. Do you think he will hang back because of you?
The only way to rebuild the trust would be to have open and honest communication. You would have to believe that he is being truthful whenever you might ask him questions about what he has been doing. He would have to understand that it will take some time before you can trust him again. It will mean you will ask him questions and at times need extra reassurance until you are able to work through it and it slowly becomes less and less of a concern. Do you think he is willing to do that? Do you think you could work through it when he is away?
Maybe save yourself a good deal of heartache and worry and just let this one go. It may be hard at first, but once he is gone it will get easier. Then you won't even have to worry and wonder about what he may or may not be doing.
There are so many other guys out there that you could have a healthy and honest relationship with.