Inspired by Numberphile

Number Theory Level pending

Joe lost a bet to Bob. He had to pay a huge amount of candy! Here's how he went about it:

On the first day of school, Joe gave 1 piece of candy to Bob. On the second day, Joe gave 1 piece of candy to Bob. On the third day, Joe gave 2 pieces of candy to Bob. On the fourth day, Joe gave 3 pieces of candy to Bob. On the fifth day, Joe gave 5 pieces of candy to Bob.

In general, on the \(nth\) day he gave \(F_n\) pieces of candy, where \(F_n\) is the \(nth\) Fibonacci number. Joe pays like this until the 180th day of school.

In total he payed \(x\) pieces of candy to Bob. Find \(x\) \((mod 3)\)

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