To solve the equation sinx + 2sinxcosx - 4cosx - 2 = 0, we can first rewrite it in terms of sine and cosine functions:

sinx + 2sinxcosx - 4cosx - 2 = 0

Rearranging terms:

sinx + 2sinxcosx - 4cosx = 2

Using the trigonometric identity sin(A + B) = sinAcosB + cosAsinB:

sinx + sin(2x) - 4cosx = 2

Now, using the double angle identities sin(2x) = 2sinxcosx and cos(2x) = 1 - 2sin^2(x), we can rewrite the equation:

sinx + 2sinxcosx - 4cosx = 2

Expand the equation:

sinx + 2sinxcosx - 4cosx = 2

Now, we can substitute cosx with 1 - sin^2(x) to rewrite the equation in terms of sinx:

sinx + 2sinx(1 - sin^2(x)) - 4(1 - sin^2(x)) = 2

simplify the equation:

sinx + 2sinx - 2sin^3(x) - 4 + 4sin^2(x) = 2

Rearrange terms:

2sinx + 4sin^2(x) - 2sin^3(x) = 6

Now that the equation is in terms of sinx, we can try to solve it further.