Sometimes expanding stuffs is very helpful!

Geometry Level 4

Given that \[A, B,C\] are such real numbers for which all trigonometric functions are defined and \[ \dfrac{\tan(A-B)}{\tan(A)} + \dfrac{\sin^{2}(C)}{\sin^{2}(A)} = 1\], then the expression \[\tan(A) \cdot \tan(B)\] is equal to:

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