2022 SSMO Team Round Problems/Problem 7

Problem

Let $\cos(2A)$ , $\cos(2B)$ , and $\cos(2C)$ be the not necessarily distinct roots of a monic cubic $f$ . Given that $f(1)= \frac{17}{30}$ , the value of $\sin(A)\sin(B)\sin(C)$ can be expressed as $\frac{\sqrt{m}}{n},$ with $m$ squarefree. Find $m+n$ .

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2022 SSMO Team Round Problems/Problem 7

Problem

Solution