How to solve trigonometric equations using gatool?

I am trying to solve harmonic elimination equation and it contains three variables t1,t2,t3 and three equations. the equations are

cos(t1)+cos(t2)+cos(t3)=m;
cos5(t1)+cos5(t2)+cos 5(t3)=0;
cos 7(t1)+cos (t2)+cos 7(t3)=0;

how to solve these three equations using GATOOL? Constraint is t1<t2<t3<90

[John D'Errico]

Does this have some mathematical meaning?

cos5(t1)

If you create your own notation, don't expect others to know what it means. For example, I have no idea if your intent is to write cos(5*t1), or if you really wanted to write (cos(t1))^5. And surely if I were to guess, my guess would be wrong.

In addition, while you state that

t1<t2<t3<90

There is no information provided about t1. May it take on any value as long as it is less than t2?

And finally, I see that your third equation has what appears to be an inconsistency. Is the second term in that equation written properly, or did you forget to type a 7 there?