View source for 2022 SSMO Team Round Problems/Problem 7

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

==Solution==