Find the sum of series `co sec theta+co sec 2 theta+co sec 4 theta+.......` to n terms

Explanation

`co sec theta=(1)/(sin theta)=(1)/(sin theta)(sin theta//2)/(sin theta//2)`
`=(sin(theta-(theta)/(2)))/(sin thetasin((theta)/(2)))=(sin thetacos((theta)/(2))-costheta sin((theta)/(2)))/(sin tehta sin ((theta)/(2))`
`therefore co sec theta=cot (theta)/(2)-cot theta`.
Similarly, `co sec2 theta=cot theta-cot 2 theta`
`co sec 4 theta=cot 2 theta-cot 4 theta`
`co sec 2^(n-1)theta=cot2^(n-2)theta-cot2^(n-1)theta`
`therefore Sum =cot""(theta)/(2)-cot2^(n-1)theta`