Let $\theta$ be the smallest acute angle for which $\sin \theta,$ $\sin 2 \theta,$ $\sin 3 \theta$ form an arithmetic progression, in some order.  Find $\cos \theta.$The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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