A320 EXECUTED GAR AT LAX RWY 25R AFTER ENCOUNTERING WAKE TURB FROM A B777 DEP RESULTING FROM A QUESTIONABLE SPACING CALL BY ATC.

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WE WERE ON THE ILS RWY 25R (RWY 25L CLOSED FOR REPAIRS) AND HEARD TWR ASK DEPARTING ACR FLT IF THEY COULD ENTER DIFFERENT SID FOR DEP. THEY REPLIED THAT IT WOULD TAKE ABOUT 30 SECONDS AND TWR GAVE THEM THE NEW SID. MEANWHILE WE ARE ON THE APCH IFR AND ARE CLRED TO LAND. WHEN FLT Y HAD THE NEW SID ENTERED; ATC CLRED THEM FOR TKOF. WHEN WE BROKE OUT OF THE BASES AT APPROX 1100 FT AGL THE B777 WAS STILL ON THE TXWY. WHEN WE WERE APPROX 800 FT AGL; LAX TWR CLRED THE B777 FOR AN IMMEDIATE TKOF. AT THIS POINT THEY WERE STILL ON THE TXWY. THE FO WAS FLYING AND CONTINUED THE APCH. WE WERE EXPECTING GAR INSTRUCTION FROM THE TWR BUT THEY NEVER ISSUED A GAR AND WE CONTINUED THE APCH SINCE THE GAR WOULD PUT US OVER THE DEPARTING B777. AT APPROX 100 FT THE B777 WAS STARTING TO ROTATE AND WE WOULD HAVE A CLR RWY TO LAND; BUT WE STARTED GETTING INTO TURB FROM THE DEPARTING B777. THE FO INITIATED A GAR; AT THIS TIME WE WERE APPROX 1 MI BEHIND THE B777 AND LESS THAN 100 FT. THE TWR GAVE USA L TURN TO 235 DEGS (NOTE: TURN BEFORE THE SMO 160 DEG RADIAL) AND THE B777 A 250 DEG HDG FOR SEPARATION. WE RETURNED FOR AN UNEVENTFUL LNDG ON RWY 25R. THE TWR DID APOLOGIZE FOR THE PREVIOUS GAR BUT SHOULD HAVE CANCELED THE TKOF CLRNC FOR THE B777 SINCE THEY WERE DELAYING THEIR TKOF AND HAD NOT ENTERED THE RWY. DUE TO RWY 25L BEING CLOSED AND LAX TWR NOT ACCUSTOMED TO LNDG AND DEPARTING THE SAME RWY; I EXPECT A LEARNING CURVE ON THEIR PART FOR THE REQUIRED SEPARATION.