Question

Solve the equation
tan²3Θ = cot²a

Answer 1

this can't be sovled there are two variables and one equation

Answer 2

assuming a typo and you meant

tan^2 3a = cot^2 a

good luck. wolframalpha solves it, and you get

a = 2πn ± 2 arctan(1 ± √2)
and
a = 2πn ± 2 arctan(1 - √2 - √(4-2√2))

Answer 3

Making the same assumption as Steve,
recall that tan 45° and cot 45° = 1
as a matter of fact , both the tangent and cotangent of any ODD multiple of 45 is either +1 or -1
since both sides of the equation are squared, any multiple of 45° or π/4 radians will be a solution

e.g. let a = 495° (45x11)
LS = tan^2 (1485) = 1
RS = tan^2 (495) = (-1)^2 = 1

If we take even multiples of 45° we run into undefined situations in either the tangent or the cotangent
if the multiple is even and divisible by 4, then the
tangent is zero, but the cotangent would be undefined.
if the multiple is even and not divisible by 4, then the tangent is undefined, (cotangent would be zero)

Using the webpage that Steve suggested
http://www.wolframalpha.com/input/?i=%28tan%283x%29%29%5E2-1%2F%28tan%28x%29%29%5E2%3D0

shows that 22.5° or π/8 radians is also a solution.
A similar analysis of multiple of 22.5 can also be made