Find the maximum value of `|[1, 1, 1],[ 1, 1+sintheta,1],[ 1, 1, 1+costheta]|`

Explanation

`D = |[1,1,1],[1,1+sintheta,1],[1,1,1+costheta]|`

Applying `R_2->R_2-R_1` and `R_3->R_3-R_1`


`= |[1,1,1],[0,sintheta,0],[0,0,costheta]|`

`=[1(sinthetacostheta-0)-0+0] `

`=sinthetacostheta`

As `sinxcosx = 1/2sin2x`

`:. D=1/2sin2theta`

We know maximum value of `sin2theta` will be `1`.

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