It is obvious from figure that angle between T and W is (180-theta). Again the angle between T and F will be (90+theta)
So by Lami's theorem
T/sin90 = F/sin(180-theta)= W/sin(90+theta)
=> T=F/sin (theta)=W/cos(theta)
Tsin(theta)= F andTcos(theta)=W
Hence tan(theta)=F/W
So (theta) = arctan(F/W)
And T= √(F^2+W^2) N