FLAG 2a: ( 1003)
It is Black's choice to play the Hanezeki Exchange (, ) with move .

FLAG 2a1:
With the double throw-in, this will have no effect, so Black still needs one external ko-threat.

FLAG 2a2:
However, there might be sub-variations, where playing the Hanezeki Exchange was not correct technically.

FLAG 2b: ( 1005)
It is White's choice to play the gote-sente-combination , , in the hanezeki.

With the double throw-in, this will have no effect, so Black still needs one external ko-threat.
FLAG 2b1:
However, the gote-sente-combination is mandatory with no throw-in, as shown earlier ( 1001)!

FLAG 2b2:
With the double throw-in, the moves inside the hanezeki do not matter.