So I'm not sure if this is a simple question to solve, but I was going through some exam review for my upcoming Linear Algebra exam and I came across this question.
What is the determinant of the following matrix?
$$ \begin{vmatrix} 1 & 1 & 1 \\ \sin^2(a) & \sin^2(b) & \sin^2(c) \\ \cos^2(a) & \cos^2(b) & \cos^2(c) \\ \end{vmatrix} $$
We never went over anything like this in lecture, so I am at a loss as to where I should even start.
I found this example but its not quite the same as this question.
Hint: What is the sum of the second and third row?