How can I verify this identity?

identity See file.
Computer GuyAsked:
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d-glitchConnect With a Mentor Commented:
If you let   y =2x , then   tan(4x) = tan(2y)

If you apply the the double angle formula as ozo has suggested, you will get an expression in terms of   tan(y) = tan(2x)

If you can apply the double angle formula again, you will get a slightly messy expression which can be simplified to the given form.

This is a slightly more involved three or four step proof.
Checking it at several values of x could lend some validity to it.
Computer GuyAuthor Commented:
Please list some steps.
Or verify the double angle tangent identity here:
and apply it twice
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