If f(x)=cosec⁡(x+π/3)cosec⁡(x+π/6) then the value of ∫0π/2 f(x)dx is

I=∫0π/2 cosec⁡(x+π/3)cosec⁡(x+π/6)dx=1sin⁡(π/6)∫0π/2 sin⁡[(x+π/3)−(x+π/6)sin⁡(x+π/3)sin⁡(x+π/6)dx=2∫0π/2 [cot⁡(x+π/6)−cot⁡(x+π/3)]dx=2log⁡sin⁡(x+π/6)sin⁡(x+π/3)0π/2=2log⁡3/21/2−log⁡1/23/3=2log⁡3