How can I find the radius of curvature of a pipe when given the angle?

Here's some visual guidance:

We thus must have that

$$ R = 1.5 + R \cos{69º} $$

The circular arc before hitting the wall describes a sector of a circle with radius $r$ and angle $\theta$. One radius of the sector is straight vertical, and the other intersects the wall perpendicular to the wall. We therefore have $$\theta + 90 + (90-69) = 180$$ and so $\theta = 69$ degrees. Finally $$r\cos\theta = r-1.5$$ or $$r = \frac{1.5}{1-\cos 69^\circ} \approx ~2.34\ \mathrm{mm}$$

(Sanity check: if $69^\circ$ were $90^\circ$ instead, the above would give $r=1.5\ \mathrm{mm}$, which is as expected.)