# Product of Sine and Cosine

Geometry Level 2

$$\sin\left(\frac{\pi}{8}\right)\cos\left(\frac{\pi}{8}\right) = \frac{a\sqrt{b}}{c}$$, where $$a, b$$ and $$c$$ are integers such that $$a$$ and $$c$$ are coprime, and $$b$$ is not divisible by the square of any prime. What is the value of $$a+b+c$$?

Details and assumptions

$$a, b$$ and $$c$$ are allowed to be 1. In particular, if you think the value is $$1 = \frac {1 \sqrt{1} } {1}$$, then $$a+b+c=1+1+1=3$$.

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