HOW TO COMPUTE THIS EQUALITY

[raymond]

why pi+2arctan((-sinx)/(1-cosx)) become to pi-2arctan(sinx/(1-cosx))?

 

[lev888]

arctan(-x) = - arctan(x)

 

[Steven G]

why pi+2arctan((-sinx)/(1-cosx)) become to pi-2arctan(sinx/(1-cosx))?
View attachment 15273

You need to look and see what changes were made. The addition sign become subtraction and the -sin(x) become sin(x). This means exactly what lev888 said, that arctan(-x) = - arctan(x) since somehow that - in the numerator magically came out in front.