Try this option (replace, pls, a↔θ):
rule: if a∈[0;90°], then cos(a)>0, sin(a)>0, sin(a/2)>0, cos(a/2)>0 and tg(a)>0.
1. for sin(a/2):
using 'cos(a)=1-2sin²(a/2)', ⇒
[tex]sin \frac{a}{2}= \sqrt{ \frac{1-cos(a)}{2}};
[tex]sin \frac{a}{2}= \frac{3}{ \sqrt{34}} .[/tex]
2. for sin(2a):
sin(2a)=2*sin(a)cos(a), where sin(a)=√(1-cos²(a))=15/17.
[tex]sin(2a)=2* \frac{15}{17}* \frac{8}{17}= \frac{240}{289}.[/tex]
