A coin is altered so that the probability that it lands on heads is less than than \dfrac{1}{2} and when the coin is flipped four times, the probability of an equal number of heads and tails is \dfrac{1}{6}. What is the probability that the coin lands on heads?
Answer Choices
A. \dfrac{\sqrt{15}-3}{6}
B. \dfrac{6-\sqrt{6 \sqrt{6}+2}}{12}
C. \dfrac{\sqrt{2}-1}{2}
D. \dfrac{3-\sqrt{3}}{6}
E. \dfrac{\sqrt{3}-1}{2}