In triangle \(TUX\), \(TU=\sqrt5+1\) cm and \(TX=3\sqrt5-2\) cm.
Given that the area of the triangle \(TUX\) is \(6\text{ cm}^2\), find the value of \(\sin XTU\), giving your answer in the form of \(\dfrac{a+b\sqrt5}{c}\) where \(a\), \(b\) and \(c\) are integers.[6]
Hence or otherwise, calculate the possible values of angle \(XTU\).[1]