A crazed repeat offender flashed a devilish grin as he made his first court appearance Saturday for allegedly shoving an elderly, retired teacher down an NYC subway stairwell, killing him.

Rhamell Burke, who’s been arrested four times since February, showed no remorse at his arraignment on murder charges for the random attack against retired teacher Ross Falzone .

Rhamell Burke (above) flashed a delilish grin in court after allegedly shoving and killing a man in a Manhattan subway station. Michael Nagle for NY Post

The victim was 76-year-old retired teacher Ross Falzone.…