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I'm pretty sure that your assumption that a servo can turn 270 degrees is wrong!
normal RC-servos turn 180 degrees some servo maybe 190 degrees.
Or if it is a continous rotation servo it will go on spinning and spinning and spinning.
Anyway you have to specify which exact type of servo you are using.
maybe now a days some digital servos are able to turn 270 degrees on an expanded pulsewith-range.
The standard servo-library limits the pulsewith from 1000 to 2000 microseconds. You can change this but it is unlikely that a standard RC-servo can cope with shorter pulses than 600 microseconds or longer pulses than 2400 microseconds.