# Ratio of trigonometric expression

If $$displaystyle theta_ {k} = frac {2 ^ {k-1} pi} {2 ^ n + 1}$$ and $$displaystyle a_ {k} = sec ^ 2 ( theta_ {k})$$ and $$displaystyle b_ {k} = csc ^ 2 ( theta_ {k}).$$

Then value of $$displaystyle frac { sum ^ {n} _ {k = 1} a_ {k}} { sum ^ {n} _ {k = 1} b_ {k}}.$$

what I try

$$sec ^ 2 bigg ( frac { pi} {2 ^ n + 1} bigg) + sec ^ 2 bigg ( frac {2 pi} {2 ^ n + 1} bigg) + cdots + sec ^ 2 bigg ( frac {2 ^ {n-1}} {2 ^ n + 1} bigg).$$