What is the value of $\begin{vmatrix} 3\sin\theta & -3\cos\theta \\ \cos\theta & \sin\theta \end{vmatrix}$?

Explanation

1. 01

   $3\sin\theta \cdot \sin\theta - (-3\cos\theta)(\cos\theta) = 3\sin^2\theta + 3\cos^2\theta$.

2. 02

   $= 3(\sin^2\theta + \cos^2\theta) = 3$, whatever $\theta$ is.