Is set {x, sinx, sin2x,}in C[0,1] linearly dependent or independent?

Is set {x, sinx, sin2x,}in C[0,1] linearly dependent or independent?

I understand the problem is to show if

c1v1+c2v2+c3v3=0

in this case

c1x + c2sinx + c3sin2x=0

has more than the trivial solution in the space of all continouse functions in [0,1]. In otherwords can I find at least one non-zero c coefficient to satisfy this equation?

What is the best way to approach this? Can I plug in numbers for x and see if any of the c's are non-zero. The non-trivial solution should work for all x's so if I show it doesn't work for specific x's in the interval then the solution must be trivial? Or can I define another continous function in the interval = function 1 (dot product) function 2 then say these are orthogonal hence = 0 and find c's that way?

Thanks

My intution tells me they are independent but math is all about showing proof. Its just when I look at the graph of these on 0,1 interval I can't see how any of the functions can be a linear combination of the other two.