Linear Independence of Secant-squared or tangent-squared Due to a result from Chowla, we know that the set $\cot(2\pi k/n)$, such that $\gcd(k, n) = 1$, is linearly independent over the Rationals.

Do we have any similar results for $\sec^2(2\pi k/n)$ or $\tan^2(2\pi k/n)$ ?

Thanks
K. Wang, On a theorem of S. Chowla, J. Number of theory 15 (1982), 1-4
all the derivatives of cot(x) which includes sec-squared and hence tan-sqared.
K. Wang, On a theorem of S. Chowla, J. Number of theory 15 (1982), 1-4
all the derivatives of cot(x) which includes sec-squared and hence tan-sqared.