Q: Find the value of infinite product $(2\cos(\frac{\pi}{9})-1)(2\cos(\frac{\pi}{27})-1)\cdot\cdot\cdot(2\cos(\frac{\pi}{3^{n+1}})-1)\cdot\cdot\cdot$ It is actually part 2 of a two-parter question. The first part was to solve the equation, $$4x^{3}-3x+1$$ The instructions are to use the results from the first part to evaluate the infinite product
$$(2\cos(\frac{\pi}{9})-1)(2\cos(\frac{\pi}{27})-1)\cdot\cdot\cdot(2\cos(\frac{\pi}{3^{n+1}})-1)\cdot\cdot\cdot$$
My Progress (really little):

*

*If I'm not wrong the $4x^{3}-3x+1$ can be factorised as $(x+1)(2x-1)^{2}$

*$(2cos(\frac{\pi}{3^{n}})-1)$ = $(2cos(3\frac{\pi}{3^{n-1}}) + 1)- 3) = 2(4cos^{3}(\frac{\pi}{3^{n-1}})-3cos(\frac{\pi}{3^{n-1}})+1)-3$ with contents inside the bracket awfully like the first equation.

