IDK about you but I'd rather get no apology than get an insincere one that fails to admit fault.
But before we even start, take a deep breath and emotionally prepare yourself to admit fault.
As Winch explains, the point of an apology is “to ease that person’s emotional burden and garner their authentic forgiveness.” That really isn't NBD, so get your head right. Take some time to think about what you’re about to do and imagine what it’ll be like to, for example, absorb someone's anger or hurt.
Cool? Cool, here we go.