Answer
There are no solutions.
Work Step by Step
$8~sec^2~\frac{x}{2} = 4$
$sec^2~\frac{x}{2} = \frac{1}{2}$
$sec~\frac{x}{2} = \pm~\sqrt{\frac{1}{2}}$
However, there is no angle $\frac{x}{2}$ such that $\vert sec ~\frac{x}{2}\vert \lt 1$. Therefore, there are no solutions.