Find all values of \( k, x \) and \( y \) for which the system of equations satisfies \[ \begin{...

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Find all values of \( k, x \) and \( y \) for which the system of equations satisfies
\[
\begin{aligned}
\sin x \cos 2 y & =\left(k^{2}-1\right)^{2}+1 \\
-\cos x \sin 2 y & =k+1
\end{aligned}
\]
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