If phi is the angle of 3rd quadrant then
cosphi->-ve and sinphi->-ve
Now sin2phi=2sinphicosphi
=-2sqrt(1-cos^2phi)*cosphi
=-2sqrt(1-(-15/17)^2)*(-15/17)
=+2sqrt(17^2-15^2)/17*xx15/17
=(2*8*15)/17^2=240/289
2phi=sin^-1(240/289)
~~56.14^@color(red)(->2phi" is in the 1st quadrant")
Again
cosphi=-15/17
phi=cos^-1(-15/17)=360-151.93=208.07
color(red)(("As "phi" is in the 3rd quadrant"))
:.2phi=416.14=360+56
.14
So 2phi is the angle of 1st quadrant.