Transmission and method for control of boost spool

A method of operating a gas turbine engine of an aircraft, the gas turbine engine comprising:

• a first spool comprising a first compressor and a first turbine mounted to a first shaft;
• a second spool comprising a second compressor and a second turbine mounted to a second shaft;
• a third spool comprising a third compressor and a third turbine mounted to a third shaft;
• an accessor gearbox comprising a housing, a first gearing and a second gearing, the first gearing and the second gearing enclosed within the housing, wherein the first clearing rotates independently of the second clearing;
• a plurality of engine accessories;
• and
• wherein the first spool is rotationally coupled to the plurality of engine accessories via the first gearing;
• and
• wherein the third spool is rotationally coupled to the second spool via the second clearing, the gas turbine engine having an operational power range that includes an intermediate power range between a maximum continuous power and a minimum continuous power, the method comprising:
• supplying fuel at a first fuel flow rate to a primary combustor of the gas turbine engine contemporaneously with supplying fuel at a second fuel flow rate to a secondary combustor of the gas turbine engine based on a power lever angle indicative of the intermediate power range,
• wherein:
• the first fuel flow rate varies to maintain a minimum exhaust pressure ratio of the gas turbine engine;
• the second fuel flow rate varies based on a power lever angle greater than loiter power and less than or equal to cruise power;
• the primary combustor is disposed between the first compressor and the first turbine and fluidly communicates with the first compressor and the first turbine;
• the secondary combustor is disposed between the second compressor and the second turbine and fluidly communicates with the second compressor and the second turbine;
• and
• the second shaft is not coaxial with the first shaft.