To simplify the given expression, we will first use the trigonometric identity formula:
sin^2(x) = (1 - cos(2x))/2

Now, substitute this identity into the given expression:

Sin(6x) + sin(2x) + 2((1 - cos(2x))/2) = 1
sin(6x) + sin(2x) + 1 - cos(2x) = 1

Rearrange the terms:
sin(6x) + sin(2x) - cos(2x) = 0

Apply the sum-to-product formula:
sin(a) + sin(b) = 2sin((a+b)/2)cos((a-b)/2)
sin(6x) + sin(2x) = 2sin((6x+2x)/2)cos((6x-2x)/2)
sin(6x) + sin(2x) = 2sin(4x)cos(2x)
sin(6x) + sin(2x) = 2(2sin(2x)cos(2x))cos(2x)
sin(6x) + sin(2x) = 4sin(2x)cos^2(2x)

sin(6x) + sin(2x) - cos(2x) = 4sin(2x)cos^2(2x) - cos(2x)

Factor out cos(2x) from the right side:
sin(6x) + sin(2x) - cos(2x) = cos(2x)(4sin(2x)cos(2x) - 1)

Therefore, the simplified expression is:
sin(6x) + sin(2x) - cos(2x) = cos(2x)(4sin(2x)cos(2x) - 1)