Trigonometric identity

Hi, please could i have help on this question? I divided both sides by tan theta and got cos theta=1/2 and found the solutions but the markscheme also has sin thet=0 but I don’t get where that came from?
Here is the question; https://app.gemoo.com/share/image-annotation/592087963147464704?codeId=M0G6nRA2V4VRY&origin=imageurlgenerator

Here is the markscheme: https://app.gemoo.com/share/image-annotation/592088707225399296?codeId=M0G6nndgLWBlg&origin=imageurlgenerator

Thank you!

You divided out the extra solution. So factorise tan(theta) and reason about the values of each factor.