Without expanding, show that the value of each of the following determinants is zero: \[ \left|\...

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Without expanding, show that the value of each of the following determinants is zero:
\[
\left|\begin{array}{lll}
\sin \alpha & \cos \alpha & \cos (\alpha+\delta) \\
\sin \beta & \cos \beta & \cos (\beta+\delta) \\
\sin \gamma & \cos \gamma & \cos (\gamma+\delta)
\end{array}\right|
\]
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