If
cos
⁡
θ
=
4
27
cosθ=
27


4

and angle
θ
θ is in Quadrant I, what is the exact value of
tan
⁡
2
θ
tan2θ in simplest radical form?

What is the sum of the geometric series in which a1 = 7, r = 3, and an = 1,701? hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio