(2/√3)(tgx-ctgx)=tg²x+ctg²x-2
(2/√3)(tgx-ctgx)=(tgx-ctgx)²
2/√3)(tgx-ctgx)-(tgx-ctgx)²=0
(tgx-ctgx)(2/√3-tgx+ctgx)=0
tgx-1/tgx=0
(tg²x-1)/tgx=0
(tgx-1)(tgx+1)=0,tgx≠0
tgx=1⇒x=π/4+πk,k∈z
tgx=-1⇒x=-π/4+πk,k∈z
2/√3-tgx+1/tgx=0
2tgx-√3tg²x+√3=0
tgx=a
√3a²-2a-√3=0
D=4+12=16
a1=(2-4)/2√3=-1/√3⇒tgx=-1/√3⇒x=-π/6+πk,k∈z
a2=(2+4)/2√3=√3⇒tgx=√3⇒x=π/3+πk,k∈z