I don't use PeasyCam so I didn't look too hard at your code, but you can't just add another trig function to control the z-axis. You'll have to look into Spherical Coordinates:  http://en.wikipedia.org/wiki/Spherical_coordinate_system

thanks, and looks cool but not helpfull.
I changed the code so no peasy is needed:

1. import processing.opengl.*;
2. // coordinates for the bezier
3. float x1 = 72;
4. float y1 = 127;
5. float z1 = 200;
6. float cx1 = 57;
7. float cy1 = 190;
8. float cz1 = 0;
9. float cx2 = 517;
10. float cy2 = 104;
11. float cz2 = 0;
12. float x2 = 283;
13. float y2 = 273;
14. float z2 = 80;
15. void setup() {
16.   size(500, 500, OPENGL);
17.   smooth();
18. }
19. void draw() {
20.   background(0);
21.   lights();
22.   translate(width/2, height/2);
23.   rotateY(map(mouseX, 0, width, 0, TWO_PI));
24.   rotateX(map(mouseY, 0, height, 0, TWO_PI));
25.  
26.   translate(-100, -100);
27.  
28.   noFill();
29.   stroke(255);
30.   bezier(x1, y1, z1, cx1, cy1, cz1, cx2, cy2, cz2, x2, y2, z2);
31.   int steps = 10;
32.   PVector bp, bt; // bezierPoint, bezierTangent
33.    noStroke();
34.   fill(255, 0, 0);
35.   for (int i = 0; i <= steps; i++) {
36.     float t = i / (float)steps;
37.     bp = bezierPoint(x1, y1, z1, cx1, cy1, cz1, cx2, cy2, cz2, x2, y2, z2, t);
38.     bt = bezierTangent(x1, y1, z1, cx1, cy1, cz1, cx2, cy2, cz2, x2, y2, z2, t);
39.     float a1 = atan2(bt.y, bt.x);
40.     a1 += HALF_PI;
41.    
42.     // angle seen from xz
43.     float a2 = PApplet.atan2(bt.z, bt.x);
44.     a2 += PApplet.HALF_PI;
45.    
46.     stroke(0, 255, 0);
47.     line(bp.x, bp.y, bp.z, bp.x + cos(a1)*-8, bp.y + sin(a1)*-8, bp.z + sin(a2)*-8);
48.   }
49.  
50.   // handle lines
51.   stroke(0, 0, 255);
52.   line(x1, y1, z1, cx1, cy1, cz1);
53.   line(x2, y2, z2, cx2, cy2, cz2);
54. }
55. // . . . . . . . . . . . . . . . . . . . . . . . .
56. PVector bezierPoint(float x1, float y1, float z1, float cx1, float cy1, float cz1, float cx2, float cy2, float cz2, float x2, float y2, float z2, float t) {
57.   PVector returnVector = new PVector();
58.   returnVector.x = bezierPoint(x1, cx1, cx2, x2, t);
59.   returnVector.y = bezierPoint(y1, cy1, cy2, y2, t);
60.   returnVector.z = bezierPoint(z1, cz1, cz2, z2, t);
61.   return returnVector;
62. }
63. // . . . . . . . . . . . . . . . . . . . . . . . .
64. PVector bezierTangent(float x1, float y1, float z1, float cx1, float cy1, float cz1, float cx2, float cy2, float cz2, float x2, float y2, float z2, float t) {
65.   PVector returnVector = new PVector();
66.   returnVector.x = bezierTangent(x1, cx1, cx2, x2, t);
67.   returnVector.y = bezierTangent(y1, cy1, cy2, y2, t);
68.   returnVector.z = bezierTangent(z1, cz1, cz2, z2, t);
69.   return returnVector;
70. }