Step 1: e i * pi = -1
Step 2: e i * pi + 1 = 0
Step 3: e 3i * pi + e 2i * pi = 0 (multiplying by e 2i * pi)
Step 4: 3e 3i * pi + 3e 2i * pi = 0 (multiplying by 3 )
Step 5: 2e 3i * pi + 2e 2i * pi = 0 (multiplying equation in step 3 by 2 )
Step 6: 2e 3i * pi + 2e 2i * pi = 3e 3i * pi + 3e2i * pi (noting LHS of step 4 is equal to LHS of step 5)
Step 7: 2(e 2i * pi + e i * pi ) * e i * pi = 3(e 2i * pi + e i * pi) * e i * pi (grouping terms)
Step 8: 2e i * pi = 3e i * pi (on dividing by (e 2i * pi + e i * pi ))
Step 9: 2 = 3 (on dividing by e i * pi )
QED