Black's sacrifice at is the key to keeping sente. Black's four in a row on the second line is good enough for an eye, and he can make the second in the space in the middle (a and b are miai).
If White responds to the cut with , she will be captured, solving Black's problems. This is a simple capturing race and Black is ahead three liberties to two.
Note also that cannot be played as in this diagram, since
puts the three black stones in atari.
The clamp at is wrong. White can connect at
, and to secure the eye on the top, Black must connect at
, this time in gote. After
, there is only one eye at the top. See six die but eight live for more information.