Find the smallest positive integer $n$ such that
\[(\cos 84^\circ + i \sin 84^\circ)^n\]is a real number.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the smallest positive integer $n$ such that
\[(\cos 84^\circ + i \sin 84^\circ)^n\]is a real number.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
15
Find the smallest positive integer $n$ such that
\[(\cos 84^\circ + i \sin 84^\circ)^n\]is a real number.
train