Must we repent in order to be forgiven?
Yes. However, It is crucial for one to have a biblical understanding of repentance?
Repent/Metanoeo: to think differently or afterwards, i.e. reconsider
Can a man change his own nature or is it the work of God?
2 Corinthians 7:10
10 For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death.
Sorrow given by God the Spirit causes you to think differently. Again, this is the new birth, quickening of the Spirit, the changing of nature and direction.
To repent is to turn from one way to another, the changing of mind, the way of thinking, it is a change of nature. It is NOT just a feeling of remorse. Though once the eyes are opened through the quickening of the spirit you are able to see the wide path you're on and true remorse will accompany you to the narrow path.
God grants repentance.
Acts 5:31
He is the one whom God exalted to His right hand as a Prince and a Savior, to grant repentance to Israel, and forgiveness of sins.
Acts 11:18
When they heard this, they quieted down and glorified God, saying, “Well then, God has granted to the Gentiles also the repentance that leads to life.”
2 Timothy 2:25
with gentleness correcting those who are in opposition, if perhaps God may grant them repentance leading to the knowledge of the truth,
Romans 2:4
Or do you think lightly of the riches of His kindness and tolerance and patience, not knowing that the kindness of God leads you to repentance?
2 Peter 3:9
The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.