What a big difference a small change can make

Geometry Level 5

I have three analog clocks. Clock 1 is correct, Clock 2 gains one minute every hour, and Clock 3 loses one minute every hour. I set them all to the correct time at 1212 AM. At 8 ⁣: ⁣208 \! : \! 20 PM, the angle between the hour and minute hands on Clock 1 is AA^{\circ}, the angle between the hour and minute hands on Clock 2 is BB^{\circ}, and the angle between the hour and minute hands on Clock 3 is CC^{\circ}. Assume 0A,B,C1800 \leq A, B, C \leq 180. Find the value of A+B+C\left \lfloor A + B + C \right \rfloor.

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