What is the value of x, where 0\leq x\lt 30^{\circ} satisfying \tan 3x\tan 6x=1?

Explanation

The equation \tan 3x \tan 6x = 1 implies \tan 6x = \cot 3x = \tan(90^\circ - 3x). Thus, 6x = 90^\circ - 3x \implies 9x = 90^\circ, giving x = 10^\circ.

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