\left|\begin{array}{c}{\Sin\end{array} \alpha , {\Cos} \alpha , {\Sin}(\alpha+\delta) ; {\Sin} \beta , {\Cos} \beta , {\Sin}(\beta+\delta) ; {\Sin} \gamma , {\Cos} \gamma , {\Sin}(\gamma+\delta) |}=. . . . . . . . . . . . . . . . . . . . . . . . . . .

1+{\Sin} \alpha {\Sin} \beta {\Sin} \gamma.

1-({\Sin} \alpha-{\Sin} \beta)({\Sin} \beta-{\Sin} \gamma)({\Sin} \gamma-{\Sin} \alpha)