To solve this equation, we first need to simplify the left side of the equation:

2sinx*cosx - 2(1 - 2sin^2x)

= 2sinxcosx - 2 + 4sin^2x
= 2sinxcosx - 2 + 4sin^2x
= 2sinx*cosx - 2 + 4sin^2x

Now, we can simplify further:

= 2sinxcosx - 2 + 4sin^2x
= 2sinxcosx - 2 + (2sinx)^2
= 2sinx*cosx - 2 + 4sin^2x

Now, the equation becomes:

2sinx*cosx - 2 + 4sin^2x = 1

To solve for x, we can rearrange the equation to form a quadratic equation in terms of sinx:

4sin^2x + 2sinx*cosx - 3 = 0

Let y = sinx, the equation becomes

4y^2 + 2y*cosx - 3 = 0

Now, we can use the quadratic formula to solve for y:

y = (-2cosx ± sqrt((2cosx)^2 - 44-3)) / 8
y = (-2*cosx ± sqrt(4cos^2x + 48))/8
y = (-cosx ± sqrt(cos^2x + 12))/4

After obtaining the values of y, we can then find x by taking the arcsine of y.