To solve this equation for x, we need to simplify the left side first using trigonometric identities.

Cos(2x) can be expanded using the double angle formula: cos(2x) = cos^2(x) - sin^2(x)
Sin(2x) can be expanded using the double angle formula: sin(2x) = 2sin(x)cos(x)

Now we rewrite the equation using the trigonometric identities:

cos^2(x) - sin^2(x) + 2sin(x)cos(x)cos(2x) = 7

Now we substitute cos^2(x) = 1 - sin^2(x) into the equation:

1 - sin^2(x) - sin^2(x) + 2sin(x)cos(x)cos(2x) = 7

Combine like terms:

1 - 2sin^2(x) + 2sin(x)cos(x)cos(2x) = 7

Rearrange the equation:

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

Divide by 2:

-sin^2(x) + sin(x)cos(x)cos(2x) = 3

We can further simplify this equation by recognizing that sin(x)cos(x) = 1/2sin(2x):

-sin^2(x) + 1/2sin(2x)cos(2x) = 3

Since sin(2x) = 2sin(x)cos(x), we can substitute this into the equation:

-sin^2(x) + 1/2 * 2sin(x)cos(x) = 3

-sin^2(x) + sin(x)cos(x) = 3

Now we solve this trigonometric equation to find the possible values of x.