Let x = cos2θ

Now

Using 1 – 2sin²θ = cos2θ and 2cos²θ – 1 = cos2θ

Now

Using sin(A + B) = sinA cosB + cosA sinB

Considering the limits,

0 < x < 1

0 < cos 2θ < 1

Now,

Differentiating w.r.t x, we get