Substitute each of the capital letters in bold by a different digit from 0 to 9 to satisfy this system of equations. All the angles are in degrees and none of the numbers can contain any leading zero.

- cos
**NE** + cos **DG** = cos **AE**, and:
- sin
**SH** + sin **AH** = sin **NH**, and:
- cos
**RR** + cos **TS** = cos **R**, and:
- sin
**ST** + sin **ET** = sin **OT**.

Well, Charlie did all the work and I get to collect the glory. I notice that in Charlie's solution,

0123456789 = HEADSTRONG.

Surely not a coincidence.