Consider the curve `C: y = sin 2x - sqrt(3)|sinx|, C` cuts the x-axis at `(a,0) , x in (-pi, pi)`.
`A_(1)` : The area bounded by the curve C and the positive x-axis between the origin and the line `x = a`.
`A_(2)` : The area bounded by the curve C and the negative x-axis between the line x = a and the origin.
Prove that `A_(1) + A_(2) +8A_(1) A_(2) = 4`.
