There is a thing called "sin"
Only for those willing to believe that there is.
Determinism enters the equation in terms of the final cause and effect between the sum of our free will choices
That's an incoherent comment; it's internally self-contradictory. If the universe is deterministic, there is no free will. If free will exists, then some future events remain undetermined.
Jesus added one more choice to this lifetime of choices, which is to repent
Repenting isn't about Jesus. When an atheistic humanist repents, he doesn't ask forgiveness from a god. He learns to forgive himself for some choice for which he feels remorse, and if possible, expresses that remorse and seeks forgiveness from his victim - not from gods.
As alluded, to repent (verb) is to feel and possibly to express remorse for one's actions. A penitent (noun) is somebody who has done this.
Moreover, penitentiaries are named such because it was hoped they would be places where people feel remorse for their actions and rehabilitate themselves.
And note that remorse is more than regret. Regret need not include remorse. I'm sure that Trump regrets some of his choices today, but feels no remorse, meaning that he hasn't and never will repent of them.
Atheists are people that have transcended god beliefs and religions and are comfortable living without them. As with sin and the fear of hell, we leave that to the believers.
They believe there is nothing but inevitable death no matter what you do or do not do.
No, we believe that there is insufficient evidence to assume that there is consciousness after death and accept the very real possibility that death extinguishes an individual consciousness. And most of us are fine with that thought. We don't suffer the existential angst of the believer who has never had to or learned to accept that possibility - you know, the kind of person who calls that hope and atheists hopeless and sees that as a good thing for the believer and an undesirable one for the unbeliever. There is no sense of hopelessness when one accepts that death may be the end. It's detachment. Those who are so afraid of death being the end that they need to hope that there is an afterlife to cope with their mortality are prisoners to that fear. Detachment from that is liberating.
One cannot control the fate of this inevitable ending, even with will power.
Correct, but that applies to the faithful as well.
eat, drink and be merry for tomorrow we may die.
The attitude is better expressed as making sure to take time to experience all that life has to offer while we can. That's obviously good advice. Denying oneself based in religious beliefs is not. Once I left Christianity and stopped going to churches, studying the Bible, praying, and tithing, I had more time and money to experience life, which for us was travel, attending concerts, visiting restaurants, and collecting fine art, all of which would be considered selfish and hedonistic in my former world, as if I owed the church anything or tasting what life had to offer was sinful. As I said, I've left that kind of thinking to others, and have no regrets. Au contraire.
One of the benefits of giving up religion and repurposing my time and modifying my goals and values was that I returned to studying electric guitar, a love of mine that I gave up once I found Jesus. I had been spending about four hours a workday and ten hours a weekend day practicing, but that ended when I became a Christian.
Once I left the religion, I took it up again, and became an accomplished guitarist with years of live performances in bands I formed. We recorded much of that, and eventually made YouTubes with stock footage to watch while listening to the music, which gives us a great sense of satisfaction and beauty today (my wife was the bass player). This was a taste of life not really available to me until I repurposed my time.
Here we are doing the song that made me want to play guitar. When I first heard this one, I thought how wonderful it must be to be able to sing such beautiful melodies with one's hands. This is what I gave up being with Jesus, and what I returned to when that chapter ended, which my former pastor surely would have disapproved of and called selfish:
How about you? If you're wrong about gods and afterlives, have the sacrifices you made in the service of those beliefs been a good choice anyway, or would you wish you had tasted more of the apple others have convinced you is forbidden?