The simultaneous equations in \(x\),\(y\), \[(\cos\theta)x - (\sin\theta)y = 2\] \[(\sin\theta)x + (\cos\theta)y = 1\] are solvable

- for all values of \(\theta\) in the range \(0 \leq \theta < 2\pi\);
- except for one value of \(\theta\) in the range \(0 \leq \theta < 2\pi\);
- except for two values of \(\theta\) in the range \(0 \leq \theta < 2\pi\);
- except for three values of \(\theta\) in the range \(0 \leq \theta < 2\pi\).

In this applet, the blue line is \(x\sin \theta + y\cos \theta = 1\), and the red line is \(x\cos \theta - y\sin \theta= 2\).

How will each of the lines change as we change \(\theta\)?

The intersection point, \(A\), represents the solution to the simultaneous equations. For which values of \(\theta\) is the point \(A\) uniquely defined?