Question 2
The first two terms of a geometric progression are
$4\sin^2\theta,\quad 8\sin^3\theta,$
where $\theta$ is an angle such that $0 \lt \theta \lt \frac{1}{6}\pi$.
Given that the sum to infinity of the progression is $\frac{1}{2}$, find the value of $\theta$. Give your answer in the form $\sin^{-1}k$, where $k$ is a rational number.
$4\sin^2\theta,\quad 8\sin^3\theta,$
where $\theta$ is an angle such that $0 \lt \theta \lt \frac{1}{6}\pi$.
Given that the sum to infinity of the progression is $\frac{1}{2}$, find the value of $\theta$. Give your answer in the form $\sin^{-1}k$, where $k$ is a rational number.
