Sine and sines and sines and

Geometry Level 5

Consider the function from the positive integers to the reals f(n)=sin1+sin2+sin3++sinnf(n)=\sin 1^{\circ}+\sin 2^{\circ}+ \sin 3^{\circ}+\cdots+\sin n^{\circ}. Find the maximum possible value of f(n)f(n) as nn ranges over all positive integers. Leave your answer to the nearest integer.

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