JEE Advance - Mathematics (1993 - No. 9)

Determine the smallest positive value of number $$x$$ (in degrees) for which $$$\tan \left( {x + {{100}^ \circ }} \right) = \tan \left( {x + {{50}^ \circ }} \right)\,\tan \left( x \right)\tan \left( {x - {{50}^ \circ }} \right).$$$