15. Two angles, \(x\) and \(y\), are acute.
$$\begin{aligned}
\sin x \cos y & = \frac { 1 + \sqrt { 3 } } { 4 }
\cos x \sin y & = \frac { - 1 + \sqrt { 3 } } { 4 }
\end{aligned}$$
- Find the exact value of \(\sin ( x + y )\).
- Find all possible pairs of values of \(x\) and \(y\), giving your answers in terms of \(\pi\). Fully justify your answer.
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