if x/tan(theta+a)=y/tan(theta+b)=z/tan(theta+c) then (x+y)/(x-y)sin^2(a-b) + (y+z)/(y-z)sin^2(b-c) + (z+x)/(z-x)sin^2(c-a) is

x/tan(theta+a)=y/tan(theta+b)=z/tan(theta+c)= k
Now you can wirte
x=k*tan(theta+a), y=k*tan(theta+b), z=k*tan(theta+c)

So now you can put the above in the equation and solve it by using basic trigo formulas….….….