Alan has no clue as to how to solve an advanced trig problem like this,
so he tries to say yours is a foolish question.

Draw a right triangle ABC with angle A = 18°, opposite side = BC = x,
and hypotenuse = 1.  That makes sin(18°)=opposite/hypotenuse = x/1 = x.
So we want to find x.



The angle C is 90°-18° = 72°, so we indicate that:



We draw an identical right triangle ABD underneath:



Next we draw CE to bisect the 72° angle C into
two 36° angles.

Let's let DE = y



Now triangles CDE is similar to triangle ACD, because they
each have a 36° angle and a 72° angle.  Also they are both isosceles.
Triangle ACE is also isosceles because it has a 36° angle at both A 
and C.  So AE=CE=CD.

Since AC=1=AD, AE = 1-y.  By similar triangles,



Cross-multiply:



Use the quadratic formula:










We take the + since the - sign gives a negative answer.





Edwin