if `a_(r) = (cos 2r pi + I sin 2 r pi)^(1//9)` then prove that
`|{:(a_(1),,a_(2),,a_(3)),a_(4) ,,a_(5),,a_(6)),( a_(7),, a_(8),,a_(9)):}|=0`

Explanation

`a_(r )=(cos 2r pi + I sin 2 rpi )^(1/9) =e^(i(2rpi)/(9))`
`:. Delta = |{:(a_(1),,a_(2),,a_(3)),(a_(4),,a_(5),,c_(6)),(a_(7),,a_(8),,a_(9)):}|=|{:(e^(i(2pi)/(9)),,e^(i(4pi)/(9)),,e^(i(6pi)/(9))),(e^(i(8pi)/(9)),,e^(i(10pi)/(9)),,e^(i(18pi)/(9))),(e^(i(14pi)/(9)),,e^(i(16pi)/(9)),,e^(i(18pi)/(9))):}|`
Now taking `e^(i(6pi)/(9))` common from `R_(2)` we get
`Delta =e^(i(6pi)/(9)) |{:(e^(i(2pi)/(9)),,e^(i(4pi)/(9)),,e^(i(6pi)/(9))),(e^(i(2pi)/(9)),,e^(i(4pi)/(9)),,e^(i(6pi)/(9))),(e^(i(14pi)/(9)),,e^(i(16pi)/(9)),,e^(i(18pi)/(9))):}|`
`(As R_(1) " and " R_(2) " are identical ")`