Given that \(\sin 3z^\circ = k\), where \(0 < k < 1\), how many values of \(z\) lie between \(0\) and \(360\)?

Given that \(X\) and \(Y\) both lie between \(0\) and \(360\), and that \(\sin X^\circ\) and \(\cos Y^\circ\) are both negative, find the values between which \(X + Y\) must lie.