BE36 AND CESSNA HAVE NMAC ON APCH IN HAZE TO EMT.

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MY STUDENT AND I FLEW A VFR XCOUNTRY FROM IWA TO L35 (BIG BEAR) TO EMT (EL MONTE) AND THEN BACK TO IWA. AS WE APCHED EMT ALONG THE I-10 FROM THE W; WE WERE INSTRUCTED BY SOCAL APCH TO SQUAWK VFR AND CONTACT EL MONTE TWR. WE CONTACTED EL MONTE TWR AND WERE GIVEN INSTRUCTIONS TO ENTER A L DOWNWIND FOR RWY 19. THE ATIS INFO AT EL MONTE TWR WAS RPTING A VISIBILITY OF 5 MI IN HAZE. DUE TO THE LOW VISIBILITY AND UNFAMILIARITY WITH THE AREA WE HAD TROUBLE SPOTTING THE ARPT AT FIRST. I TUNED IN THE EL MONTE NDB; WHICH IS LOCATED ON THE FIELD; AND WE PROCEEDED TO FLY DIRECT TO THE NDB. THE NDB NEEDLE FLIPPED AND I KNEW WE WERE DIRECTLY OVER THE ARPT; BUT I STILL COULD NOT SEE THE FIELD. I COMMUNICATED TO TWR THAT WE DID NOT HAVE THE FIELD IN SIGHT. TWR INSTRUCTED US TO IDENT AND THEN TO FLY N AND RPT THE RACE TRACK IN SIGHT (SANTA ANITA RACE TRACK -- A RPTING POINT N OF THE FIELD). WE FLEW NBOUND AND RPTED THE RACE TRACK IN SIGHT. TWR THEN INSTRUCTED US TO FOLLOW A CESSNA ON FINAL. I RPTED THE CESSNA IN SIGHT AND WE TURNED R BASE FOR RWY 19. DURING OUR R BASE TO FINAL TURN I SPOTTED ANOTHER CESSNA AT 12 O'CLOCK POS; SAME ALT; OPPOSITE DIRECTION APPROX 100 FT FROM US. I IMMEDIATELY GRABBED THE CTLS AND TURNED L TO AVOID THE CESSNA. AFTER WE WERE CLR OF THE TFC AND ESTABLISHED ON FINAL FOR RWY 19; I COMMUNICATED TO TWR WHAT HAD HAPPENED. AFTER WE HAD LANDED AND TAXIED TO TRANSIENT PARKING I APOLOGIZED TO EL MONTE GND FOR OUR INITIAL DISORIENTATION ON THE APCH TO EL MONTE; BUT I ALSO VOICED MY CONCERN ABOUT THE CESSNA TFC WHICH WE ENCOUNTERED ON FINAL. WHILE AT THE ARPT I SPOKE TO THE PLT OF THE CESSNA TFC; WHICH WE ENCOUNTERED ON FINAL. HE TOLD ME THAT ATC HAD GIVEN HIM AN INSTRUCTION TO MAKE A 360 DEG TURN IN EITHER A L OR R DIRECTION (I DON'T RECALL EXACTLY WHICH DIRECTION). HE TOLD ME THAT THEY USUALLY GIVE HIM INSTRUCTIONS TO MAKE A 360 DEG TURN IN THE OPPOSITE DIRECTION (AGAIN I DON'T REMEMBER IF HE SAID L OR R). ALTHOUGH VFR ACFT ARE RESPONSIBLE FOR AVOIDING EACH OTHER IN CLASS D AIRSPACE; IT IS MY EXPERIENCE THAT A TWR CTLR WILL ISSUE TA'S WHEN ACFT ARE IN THE VICINITY OF EACH OTHER. AFTER LISTENING TO THE TWR'S RESPONSE TO MY CONCERN ABOUT THE CESSNA TFC WE ENCOUNTERED ON FINAL AS WELL AS TALKING TO THE PLT OF THE CESSNA; ONE MIGHT ASSUME THAT THE TWR CTLR ISSUED A 360 DEG INSTRUCTION TO THE CESSNA IN THE WRONG DIRECTION OR THE PLT ACCIDENTALLY TURNED IN THE WRONG DIRECTION. THIS RESULTED IN THE CESSNA TURNING DIRECTLY INTO THE FINAL APCH PATH OF RWY 19.