What is the use of cap_set_proc() if the program needs to be run as root

Question

I am trying to unmount a usb-storage device through a c++ program, using umount2() function. Since umount2() needs administrative privileges, I implemented umount2() with cap_set_proc() as follows

  cap_t caps;
  cap_value_t cap_list[1];
  caps = cap_get_proc();
  if (caps == NULL)
      std::cout << "cap_get_proc failed: " << strerror(errno) << std::endl;
  cap_list[0] = CAP_SYS_ADMIN;
  if (cap_set_flag(caps, CAP_EFFECTIVE, 1, cap_list, CAP_SET) == -1)
      std::cout << "cap_set_flags failed: " << strerror(errno) << std::endl;
  if (cap_set_proc(caps) == -1)
      std::cout << "cap_set_proc failed: " << strerror(errno) << std::endl;
  else
  {
    while(umount2("/media/user/usb_storage_device", MNT_DETACH))
    {
      std::cout << "ERROR: " << strerror(errno) << std::endl;
      std::this_thread::sleep_for (std::chrono::seconds(2));
    }
    std::cout << "Unmounted!" << std::endl;
  }
  if (cap_free(caps) == -1)
      std::cout << "cap_free failed: " << strerror(errno) std::endl;

But when I run the above code as a normal user I get error:

"cap_set_proc failed: Operation not permitted"

But, if I run the code as a root, usb-storage device is unmounted successfully. So my question is, what is the use of using cap_set_proc() to provide administrative privileges, if the cap_set_proc() function itself needs root privileges to execute? Am I doing something wrong here?

Also,is it possible to actually use cap_set_proc() without executing the program with sudo?

Please help.