Without expanding evaluate the determinant `|[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|`

Explanation

To evaluate the determinant

\[
D = \begin{vmatrix}
\sin \alpha & \cos \alpha & \sin(\alpha + \delta) \\
\sin \beta & \cos \beta & \sin(\beta + \delta) \\
\sin \gamma & \cos \gamma & \sin(\gamma + \delta)
\end{vmatrix}
...