Find the number of solutions to
\[\sec \theta + \csc \theta = \sqrt{15}\]where $0 \le \theta \le 2 \pi.$
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<|im_start|>user
Find the number of solutions to
\[\sec \theta + \csc \theta = \sqrt{15}\]where $0 \le \theta \le 2 \pi.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Find the number of solutions to
\[\sec \theta + \csc \theta = \sqrt{15}\]where $0 \le \theta \le 2 \pi.$
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