Find the smallest positive rational number $r$ such that
\[\sum_{k=1}^{35}\sin (5k)^\circ = \tan r^\circ.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the smallest positive rational number $r$ such that
\[\sum_{k=1}^{35}\sin (5k)^\circ = \tan r^\circ.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
87.5
Find the smallest positive rational number $r$ such that
\[\sum_{k=1}^{35}\sin (5k)^\circ = \tan r^\circ.\]
train