Find the smallest positive rational number $r$ such that
\[\sum_{k=1}^{35}\sin (5k)^\circ = \tan r^\circ.\]
Question:
Find the smallest positive rational number $r$ such that
\[\sum_{k=1}^{35}\sin (5k)^\circ = \tan r^\circ.\]
Answer:
Let's think step by step.

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