How many solutions do these simultaneous trig equations have?

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

1. for all values of \(\theta\) in the range \(0 \leq \theta < 2\pi\);

2. except for one value of \(\theta\) in the range \(0 \leq \theta < 2\pi\);

3. except for two values of \(\theta\) in the range \(0 \leq \theta < 2\pi\);

4. except for three values of \(\theta\) in the range \(0 \leq \theta < 2\pi\).