pi from recursive square roots of 2

For example:

In general the coefficient should be the nth power of 2  and the recursive square root has log_2(n) 2's when it's written out, with the one minus sign and the rest plus signs... It comes from analysis of the sin(2*pi / 2^n). The result slowly approaches pi

**there might be an efficient way to calculate this on a computer because it uses all powers of 2? For example multiplying by 2 in binary is just shifting the binary number to the left one radix point...