If you have done something wrong and you brazen it out, you behave confidently in order not to appear ashamed, even though you probably do feel ashamed.
If you are caught simply argue that `everyone does it' and brazen it out... V it P
The president brazened out his misdeeds... V P n (not pron)
Stung by recent publicity, the Home Office now seems to be trying to brazen this issue out. V n P