>
> sage: def theta(dz):
> ...       angle=0;
> ...       if 0<=dz<2*r*cot(gangle) : angle= 2*arcsin(dz*tan(gangle)/2/r);
> ...       if 2*r*cot(gangle)<= dz < 2*2*r*cot(gangle) : angle= 
> 2*arcsin((dz-2*r*cot(gangle))/(cot(gangle)*2*r)) - pi;
> ...       if 2*2*r*cot(gangle)<= dz < 4*2*r*cot(gangle) : angle= 
> 2*arcsin((dz-2*2*r*cot(gangle))/(cot(gangle)*2*r)) - 2*pi;
> ...       if 0>=dz>-2*r*cot(gangle) : angle= 2*arcsin(dz*tan(gangle)/2/r);
> ...       if 2*r*cot(gangle)>= dz > -2*2*r*cot(gangle) : angle= 
> 2*arcsin((dz+2*r*cot(gangle))/(cot(gangle)*2*r)) - pi;
> ...       if 2*2*r*cot(gangle)>= dz > -4*2*r*cot(gangle) : angle= 
> 2*arcsin((dz+2*2*r*cot(gangle))/(cot(gangle)*2*r)) - 2*pi;
> ...       return angle;
> ...
>
> then executing
>
> sage: find_root(erseno(x)==0,2,10,xtol=0.01)

Try to print erseno(x)
it seems that your equation becomes 0.609368485026990==0

Robert

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