∫0π/2 sin⁡2x log⁡ tan⁡x dx is equal to

Let I=∫0π/2 sin⁡2xlog⁡tan⁡xdx-----i I=∫0π/2 sin⁡2π2−xlog⁡tan⁡π2−xdx ∵∫0a f(x)dx=∫0a f(a−x)dxI=∫0π/2 sin⁡2xlog⁡cot⁡xdx----iiOn adding Eqs. (i) and (ii), we get 2I=∫0π/2 sin⁡2xlog⁡(tan⁡xcot⁡x)dx=∫0π/2 sin⁡2xlog⁡1dx=∫0π/2 0dx⇒ I=0