show that:
$$\prod_{k=1}^{n-1}\sin{\dfrac{k\pi}{tn}}=\dfrac{\sqrt[t]{n}}{2^{n-1}}?(not, true),t\in N^{+}$$
maybe for $t$is real numbers also true?
I can show when $t=1$ case. because I use $$z^{n-1}-1=(z-x_{1})(z-x^2_{1})\cdots (z-x^{n-1}_{1}),x_{1}=\cos{\dfrac{2\pi}{n}}+i\sin{\dfrac{2\pi}{n}}$$ also see Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
But for $t\neq 1$,I can't use this identity