To get right to the point, when it comes to sharing secrets and being vulnerable, Epictetus advises us to hold our cards tight to our chest, until we've determined that we can trust other people and they are virtuous. Otherwise, just keep quiet.
We are often faced with people who try to gain our confidence who might share very personal information or a secret, in the hopes of getting us to reciprocate. These are con-men and you need to watch out for them.
"When someone seems to have talked frankly to us about his personal affairs, we are somehow impelled to reveal our own secrets to him in turn, and we regard that as being frankness.This comes about partly because, after hearing our neighbor's confidences, it seems unfair not to reply in kind by giving him a share of our own; and also because we think that we won't give such people the impression of being frank if we keep quiet about our personal affairs." (v. 1-2, p. 275)
If you are going to share your personal affairs and secrets with others, you need to be sure you can trust them. Otherwise, "it is just as if [you] had a water-tight barrel and [someone else] had one with a hole in it, and [they] came and entrusted [their] wine to [you], for [them] to store it in [your] barrel, and [they] then complained that [you] for [your] part didn't entrust [your] wine to [them]!" (v. 12, p. 276)