Missing steps in simplifying a trigonometric expression

[exequor]

can someone explain to me the stages that are missing in the expression in the attached picture. i think that it has to do with identities but in the book that i got it from did not explain clearly how they went from one line to another. i will appreciate the help very much. all i am trying to do is to understand how to go from one line to the other.

 

[arildno]

No wonder you're stuck; the lines contain a mistake. (Setting "theta"=15 in the last line yields 1.1=sin30)
The transformation of the righthand sides in line 2 to 3 is the sine summation formula