Sin52+sin90+sin142+sin232+sin322=???

Question

Sin52+sin90+sin142+sin232+sin322=???

Answer 1

2*sin(52+142)/2 * cos(142-52)/2  + 1+ 2*sin(232+322)/2*cos(322-232)/2=
2*sin(97)*cos(45)+1+2*sin(277)*cos(45)=(sin97+sin277)+1=
(sin97+sin(180+97))+1=(sin97-sin(97))+1=1