What is the way to atone for the sin of photographing a female colleague without her knowledge, given the fear of losing trust and severing the relationship if she is informed?

Taking pictures of your friend without her knowledge and sending them to your other friends without her permission is not permissible. Your remorse for this is commendable. You must repent with its conditions, including seeking her forgiveness and releasing yourself from her right. However, if you fear a greater harm, then supplicate for her frequently and strive to convince those to whom you sent the pictures to delete them. This will suffice you.