question

(c- a tanθ) = bcot2θ
(acotθ-c)= btan2θ

multiply

-c²-a²+ac(tanθ+cotθ)=b²

also,

taking
c-bcot2θ= a tanθ
btan2θ+c=acotθ

multiply both sides,

c²-b² +bc(tan2θ - cot2θ) = a²

tanθ+cotθ = sec²Î¸/tanθ = 1/(sinθcosθ)

tan2θ - cot2θ = -2 cos2θ/sin2θ.. now use these two in the problem above to eliminate theta :)

I hope this gives u the final solution