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Without expanding, show that the value of each of the following determinants is zero:
\[
\left|\begin{array}{rrr}
\sin ^{2} 23^{\circ} & \sin ^{2} 67^{\circ} & \cos 180^{\circ} \\
-\sin ^{2} 67^{\circ} & -\sin ^{2} 23^{\circ} & \cos ^{2} 180^{\circ} \\
\cos 180^{\circ} & \sin ^{2} 23^{\circ} & \sin ^{2} 67^{\circ}
\end{array}\right|
\]
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