Personally, I don't think you can do anything. He's engaged, so if he likes you it's his move to make. It is highly possible that he does like you, however - what can you do about it? It's not exactly the most advisable or smart thing to do when you're getting involved with a committed man. I suppose you could always ask him how he feels, but that could seriously complicate this situation even further. Stop being so shy around him in person and talk to him, if you want things to go your way - then you've got some hard work ahead of you.
But I wouldn't say getting involved in this situation is the best thing you can do for anyone involved.
To love is to suffer. To avoid suffering, one must not love; but then one suffers from not loving. Therefore, to love is to suffer, not to love is to suffer, to suffer is to suffer. To be happy is to love; to be happy then is to suffer, but suffering makes one unhappy; therefore to be unhappy one must love or love to suffer or suffer from too much happiness. I hope you're getting this down.