Compute
\[\sin^2 4^\circ + \sin^2 8^\circ + \sin^2 12^\circ + \dots + \sin^2 176^\circ.\]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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