The phrase "kept under one's hat" refers to a secret or information that is kept hidden from others. The antonyms of this phrase would be "revealed," "exposed," and "divulged." If you reveal something, you make it known to others, exposing it to the light of day. If you expose something, you uncover it and lay it bare for all to see. If you divulge something, you share it with others, breaking the secrecy that kept it hidden. By using these antonyms, you express a willingness to be open and honest, sharing your thoughts and feelings with those around you.
