2arcsin(x/underroot6)+arcsin(4x)=180/2

take sin of both sides and use your sum and double-angle formulas to get a polynomial in x

sin(2arcsin(x/?6)+arcsin(4x)) = 1
x = ?39 - 6

see

http://www.wolframalpha.com/input/?i=sin(2arcsin(x%2F%E2%88%9A6)%2Barcsin(4x))+%3D+1