Sin(2x + π/3) = cos2x

To solve this equation, we can use the trigonometric identity: sin(θ) = cos(π/2 - θ).

Using this identity, we can rewrite the equation as:

cos(π/2 - (2x + π/3)) = cos(2x)

Now, we can equate the angles inside the cosine function:

π/2 - (2x + π/3) = 2x

Simplifying the equation:

π/2 - 2x - π/3 = 2x

Combining like terms:

-4x + π/6 = 0

Solving for x:

-4x = -π/6

x = π/24

Therefore, the solution to the equation is x = π/24.