I tried to continue the question but again i feel i am on the wrong track. I tried to find θ by using the double angle formula and saying:

cot2θ=¼

so 1/tan2θ=¼

1/2tanθ/1-tan²θ=¼

1-tan²θ/2tanθ=¼

4(1-tan²θ) = 2tanθ

so 4tan²θ + 2tanθ - 4 = 0

2(2tanθ+2)(tanθ-1)=0

therefore 2tanθ+2 = 0

tanθ = -2/2

θ=tan ‾¹(-1)

θ=-45

and tanθ-1 = 0

θ=tan‾¹(1)

θ=45

Using my method i would also have to do this for the other equation for 2θ that i obtained earlier but the values i have got here are incorrect.

Can someone please tell me where i went wrong!

Edit i have tried to write my calculations using the Latex script:

so

so

therefore

and