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The number of real solution of the equat...

The number of real solution of the equation `sin ^(-1) ( sum _( i = 1 ) ^( oo) x ^( i +1) - x sum _( i = 1 ) ^( oo) ((x)/(2)) ^(t)) = (pi)/(2) - cos ^(-1) (sum _( l = i ) ^( oo) (- (x)/(2)) ^( t) - sum _( i = 1) ^( oo) ( -x) ^(1))` lying in the interval `(- (1)/(2) , (1)/(2))` is _________ (Here, the inverse trignometric functions `sin ^(-1) x and cos ^(-1) x` assume values in `[ - (pi)/(2) , (pi)/(2) ] and [0,pi],` respectively).

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