multiple solutions to equations involving sine

hello

i'll get straight to the problem

i'm looking for non-numerical, non-iterative methods for finding the solutions to equations such as this:

sin(pi*2^x) = sin(pi*2^(1-x)) = 0, over the range [-1 < x < 2]

in words, i'm looking for where the given functions simultaneously intersect each other and the x-axis

so,

sin(pi * 2^x) = 0

sin(pi * 2^(1-x)) = 0

pi * 2^x = c1 * pi

pi * 2^(1-x) = c2 * pi

where c1 and c2 are integers >= 0

2^x = c1

2^(1-x) = c2

..ok so clearly i'm just transforming this a little to see if i jog someone's memory

i vaguely remember something in calculus that would lead to multiple solutions..however it somehow involved integrals..does anyone know what those types of calculus equations are called? how to solve them?

*edit*

oh can't calculus find the points of intersection of a parabola and a line? can i use a similar process on my equations?