UNAUTH UNCOORD AIRSPACE ENTRY AS A C337 ATP PLT ENTERS THE CLASS D OF SLI AFTER A R DOWNWIND DEP FROM LGB; CA.

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ON VFR DEP FROM LGB; I INFORMED CLRNC DELIVERY I WAS DEPARTING VFR FOR SNA AND WAS INSTRUCTED TO CONTACT GND CTL FOR TAXI AND NOT GIVEN A SQUAWK. I CONTACTED GND CTL AND REQUESTED TAXI CLRNC SAYING MY DEST WAS SNA. I WAS CLRED TO TAXI TO RWY 25L AT D INTXN. I CALLED THE TWR FOR TKOF CLRNC; REQUESTING A L DOWNWIND FOR DEPARTING TO SNA. (I HAD DEPARTED IN A L DOWNWIND BEFORE MANY TIMES AND ALWAYS FLEW OVER THE WATER DOWN TO HUNTINGTON BEACH AND A TURN TOWARDS MILE SQUARE FOR LNDG CLRNC TO SNA; AVOIDING THE NEED TO CONTACT LOS ALAMITOS TWR.) I WAS GIVEN AN IMMEDIATE TKOF CLRNC; BUT WITH A R DOWNWIND BECAUSE OF APCHING TFC. I ACCEPTED THIS CLRNC; ASSUMING THAT MY DEP WAS BEING COORDINATED WITH SOCAL AND LOS ALAMITOS. AT APPROX 5 MI FROM LGB; I WAS TOLD TO SWITCH FREQ; BUT WAS NOT GIVEN A FREQ. I ASKED FOR AN APPROPRIATE FREQ AND WAS GIVEN A FREQ FOR SOCAL; BUT NOT FOR SLI WHOSE CTL ZONE I WAS NOW ENTERING. THE CTLR WAS BUSY SO I SWITCHED AND CONTACTED SOCAL AND AFTER 2 FREQ CHANGES WAS INFORMED BY THE CTLR THAT I SHOULD HAVE CONTACTED LOS ALAMITOS TWR. I WAS THEN DIRECTED TO FLY TO MILE SQUARE; CONTACT SNA AND LANDED WITHOUT INCIDENT. I REALIZE NOW THAT I SHOULD HAVE BEEN PREPARED TO HAVE THE FREQ FOR LOS ALAMITOS READY TO USE IF NECESSARY AND SHOULD NOT HAVE ACCEPTED A CLRNC WITHOUT ALL OF THE APPROPRIATE FREQS READY. BECAUSE I FLY OUT OF SNA (A CLASS C ARPT WHERE VFR AND IFR DEPS ARE ALWAYS COORDINATED WITH THE ADJOINING CTLING AGENCIES; I HAD ASSUMED I WOULD HAVE THE SAME DONE WHEN I WAS DROPPED BY LGB TWR). I BELIEVE THAT THE PROB WOULD NOT HAVE OCCURRED IF I HAD BEEN ADVISED BY LGB TWR TO CONTACT LOS ALAMITOS ON THE APPROPRIATE FREQ WHEN THEY DROPPED ME AT THE POINT THAT I WAS ALREADY IN ALAMEDA AIRSPACE. I HAVE LEARNED TO BE READY; BUT THIS IS A VERY COMPLEX; CONGESTED AREA AND FEEL THAT I FELL INTO A TRAP THAT COULD HAVE BEEN AVOIDED BY MY NOT ACCEPTING THE CHANGED DEP AND MY NOT ASSUMING THAT MY DEP WOULD BE COORDINATED AS IT IS IN MOST ARPTS I FLY OUT OF. A SUGGESTION BY THE LGB TWR CTLR TO CALL LOS ALAMITOS ON THE APPROPRIATE FREQ WOULD HAVE ALSO PREVENTED THIS PROB. I WILL USE THIS AS A LESSON TO MY STUDENTS.