trigo doubt

The pi/2-theta conversion part....I think it works only for first quadrant angles. Here we are considering all four quadrants.
Do correct me if I'm wrong.

that conversion is ok , it is valid for all angles

i think where u r making mistake is : taking both the natural nos as n . Take one as m and other as n. there isnt any reason for them to be equal , they may be related by some other equation.

yes qwerty that is right ..
let the answer be:
θ = Π3(m + 12)

but the problem is that both answers give different set of angles ,for example taking

m = 1 (in second solution) gives θ = Π2

whereas the first solution's answer can never yield θ = Π2 for any value of 'n'

Perhaps it would have been simpler to just use

\tan \theta \tan 2\theta =1 \Rightarrow \tan 3\theta=0

sir, i m getting 'tan3θ = ∞'... how can it be zero? plzz explain

han.. toh D^r zero hua na!!!

ya, sorry. i meant that tan 3θ would be undefined.

There is a small mistake that can happen .

tan θ x tan 2 θ = 1 may imply that ;

tan 3 θ = ∞ ,

if and only if , tan θ + tan 2 θ ≠0 ,

But in this case , can this happen ?

No , this can't happen as tan θ and tan 2 θ must have the same sign .

So the arguments hold .