Evaluate `|cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinalphacosbetasinalphasinbetacosalpha|`

Explanation

` Delta =|{:(cos alpha cos beta,,cos alphasinbeta,,-sinalpha),(-sinbeta,,cos beta,,0),(sinalpha cos beta,,sinalphasinbeta,,cos alpha):}|`
Expanding along `C_(3)` we have
`Delta =- sin alpha (-sin alpha sin^(2) beta- cos^(2) beta sin alpha)`
`+ cos alpha (cos alpha cos^(2) beta+ cos alpha sin^(2) beta)`
`=sin^(2) alpha(sin^(2)+cos^(2)beta) + cos^(2) alpha (cos^(2) beta+sin^(2) beta)`
`=sin^(2) alpha(1)+ cos^(2) alpha(1)`
`=1`