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I can do the first part no problem.

I then drew the graph, am I right in saying there is an infinite sequence because the lines intersect an infinite amount of times, because tan is periodic and has vertical asymptotes?

I have no idea about showing why the first non rivial zero is bounded like that. I would have thought the trivial zero was at the origin, and the first non trivial was in the range of 0<lambda<pi/2.

What am I not understanding here?

Thanks

edit:

oh I think I'm suppose to be looking for solutions in the range of pi and 3pi/2?