In Shakespeare's Romeo and Juliet, why is Romeo so unhappy?

At the beginning of Shakespeare's Romeo and Juliet, Romeo's father, Lord Montague, tells his nephew Benvolio that he is concerned for his son. He describes Romeo's behavior as depressing because he shuts himself up in his bedroom without light, he isn't social, and he seems depressed. Benvolio tells his uncle that he will find out why Romeo seems so unhappy. The interchange between Benvolio and Romeo is as follows:

"'What sadness lengthens Romeo's hours?'

'Not having that which, having, makes them short.'

'In love.'

'Out.'

'Of love?

'Out of her favour where I am in love'" (I.i.156-161).

Romeo's line which explains his sadness seems ambiguous when taken out of context. With a little more explanation the audience understands that Romeo is sad because he can't have the love he wants with Rosaline. This love makes time seem short to Romeo; but without love, his hours are lengthened with sadness. The background to this scene is explained later as Romeo tells Benvolio that Rosaline chose to be nun, which abruptly ended their relationship. Romeo is also upset that such a beautiful girl would desire to become a nun and not share her beauty with the world--or him. Of Rosaline's determination to live a chaste life, Romeo is greatly saddened and says the following:

"She hath forsworn to love, and in that vow

Do I live dead, that live to tell it now" (I.i.216-217).

The fact that Romeo feels like his life is more dead than alive is another way of saying that he is unhappy; and within the context of the conversation about Rosaline forswearing to love again, here is his reason for sadness.