The diagram shows the prism $$\(A B C D E F G H J K\)$$ with horizontal base $$\(A E F G\)$$ Diagram NOT accurately drawn $$\(A B C D E\)$$ is a cross section of the prism where $$\(A B D E\)$$ is a square $$\(B C D\)$$ is an equilateral triangle $$\(E F=2 \times A E\)$$ $$\(M\)$$ is the midpoint of $$\(G F\)$$ so that $$\(J M\)$$ is vertical. Angle $$\(M A J=y^{\circ}\)$$ Given that $$\(\quad \tan y^{\circ}=T\)$$ find the value of $$\(T\)$$, giving your answer in the form $$\(\frac{\sqrt{p}+\sqrt{q}}{17} \quad\)$$ where $$\(p\)$$ and $$\(q\)$$ are integers. $$\[ T= \]$$

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