The laboratory triad here is hypocalcaemia, hyperphosphataemia and a raised parathyroid hormone. When calcium is low yet PTH is high, the gland is working hard; the problem is that the target tissues are not listening. Coupled with a high phosphate, this is the signature of pseudohypoparathyroidism, a state of end-organ resistance to PTH.
Now weigh each option as a diagnostic lever. Measuring the cyclic AMP that the kidney generates in response to injected PTH (the Ellsworth-Howard challenge) directly demonstrates the resistance and is therefore highly informative. Checking vitamin D status is useful too, because a deficient vitamin D state can also drive PTH upward, but it characteristically lowers phosphate rather than raising it, so the result helps you separate the two scenarios. Serum creatinine screens for renal failure, which produces an identical-looking picture through secondary hyperparathyroidism, so it earns its place.
Urine myoglobin, by contrast, is a marker of muscle injury and rhabdomyolysis. It tells you nothing about the parathyroid-calcium-phosphate axis and adds no diagnostic value here. The printed key naming vitamin D is incorrect, since vitamin D measurement genuinely narrows the differential; the truly redundant test is urine myoglobin.
\[\boxed{\text{Urine myoglobin}}\]