Trig Fomula

Any comment and reference about the correctness of the following
assertion will be appreciated.

Assertion: If (1) is valid then (2) is also valid under the given
conditions.

Tan kD = (u/v)^(1/2) (1)

Tan D = (m/n)^(1/2) (2)

Conditions: 0 < D < pi/2; u, v, m, n are integers each > 1 and none is
a pefect square; (u, v) = 1, (m, n) = 1.
Prime k > 3.

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