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cos8(π12)−sin8(π12) \cos^8 \left( \dfrac\pi{12} \right) - \sin^8 \left( \dfrac\pi{12} \right) cos8(12π)−sin8(12π)
If the value of the expression above is equal to abc \dfrac {a\sqrt b}c cab, where a,ba,ba,b and ccc are integers with bbb square-free and a,ba,ba,b coprime, find a+b+ca+b+ca+b+c.
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