yeah.. I'm a geek. so what? Here is a wonderful way of doing it by hand using only simple identities and trig.

y = csc(theta)*(theta+cot(theta))

csc(theta)*(theta+cot(theta)) = 1/sin(theta)*(theta+1/tan(theta))

use quotient rule

>
> d(y) = (sin(theta)*0-cos(theta))*(theta+1/tan(theta))/sin(theta)^2+(1+(0-1-tan(theta)^2)/tan(theta)^2)/sin(theta);

> diff(y(x), x) = -theta*cos(theta)/sin(theta)^2-cos(theta)/(sin(theta)^2*tan(theta))-1/(sin(theta)*tan(theta)^2);

> diff(y(x), x) = -theta*cos(theta)/sin(theta)^2-cos(theta)^2/sin(theta)^3-cos(theta)^2/sin(theta)^3;

> diff(y(x), x) = -theta*cos(theta)/sin(theta)^2-2*cos(theta)^2/sin(theta)^3;

Stop it you are going to give me nightmares from Naval Nuclear Power School!!!!!
I have had those memories suppressed for over 20 years..............