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You should prove that the statement `sin(pi/3 + pi/6) = sin (pi/3) + sin (pi/6)` is not true, hence, evaluating the summation `pi/3 + pi/6` yields:

`pi/3 + pi/6 = (2pi+pi)/6 = (3pi)/6 = pi/2`

Replacing `pi/2 ` for `pi/3 + pi/6` yields:

`sin (pi/2) = sin (pi/3) + sin (pi/6)`

Since `sin (pi/2) = 1, sin (pi/3) = sqrt3/2, sin (pi/6) = 1/2` yields:

`1 = sqrt3/2 + 1/2` invalid

You may notice that replacing the corresponding values  in the given expression, yields an invalid statement.

Hence, the statement `sin(pi/3 + pi/6) = sin (pi/3) + sin (pi/6)` does not hold.

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