Inspired by Mridul Jain

Geometry Level 5

\[ \large x_n=a \sin n\theta+b\cos n\theta\]

Find \(x_7\) if the numbers \(a,\) \(b\) and \(\theta\) satisfy the following equations: \(x_1=15,\) \(x_2=3,\) and \(x_3=-12.\)