Interesting Trigonometry!!

Algebra Level 4

If\(\alpha ,\beta ,\ and \ \gamma\) are acute angles. And

\(\cos { \theta } =\quad \frac { \sin { \beta } }{ \sin { \alpha } } ,\quad \cos { \varphi } =\frac { \sin { \gamma } }{ \sin { \alpha } } \quad and\quad \cos { (\theta -\varphi ) } =\quad (\sin { \beta } .\sin { \gamma } ).\)

then find the value of \((tan ^{ 2 }{ \alpha } -tan ^{ 2 }{ \beta } -tan ^{ 2 }{ \gamma })\)

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