Does tan 75 = cot 75? if so why?

Question

I was doing a problem in my Trigonometry book and it asked me to "Find an angle (theta) that makes the following statement true." the problem was
tan (theta) =cot(45 + 2{theta}) the answer I got confused me it was tan 75 = cot 75

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Answer 1 · 2017-03-13T03:12:20

Given

$tantheta=cot(45+2theta)$

$=>cot(90-theta)=cot(45+2theta)$

$=>(90-theta)=(45+2theta)$

$=>2theta+theta=90-45=45$

$=>3theta=45$

$=>theta=45/3=15$

Inserting this value in the given condition we get

$tan15=cot(45+2 xx 15)=cot75$

Answer 2 · 2017-03-13T04:15:17

impossible

Calculator gives:
$tan 75^@ = 3.732$
$cot 75^@ = 0.269$
These real numbers can't not be equal.
The question may be misread.